In 19th century France, were police able to send people to jail without a trial, as presented in "Les Misérables"?

This is a plausible description.
Probably not 'the norm' in how it went down exactly, but easily filed under 'could have happened'.

But it is essential to not generalise this too far.

Since the revolution there was a general right for an accused to have a trial. That was copied from English law and survived throughout the 19th century unharmed until 'Vichy'.

What makes this scene plausible is that it is just for this one 'crime': prostitution.

The notion of tolérance developed naturally from the Augustinian dictum that prostitutes have a place in society, albeit the lowest one, because they channel potentially subversive passions away from socially disruptive violence. But for authority to tolerate prostitution did not mean that it condoned or officially protected this activity, or that it tacitly agreed to look the other way so as to let this useful function prosper.

On the contrary, toleration entailed strategies of enclosure and containment similar to those Parent advocated in dealing with poudrette, the refuse from water closets, or the remains of horse carcasses. A maison de tolérance was, ideally, carefully designed to process live flesh as was Parent's dissection table to process dead flesh. Indeed, Parent applied to hospital dissection rooms the same description he used for prostitution: they are, he says, “a necessary evil that must be tolerated".

The essential ambiguity in the program of toleration derives from its shaky legal support. No law on prostitution was passed in France during the entire course of the nineteenth century.

Because Article 484 of the Penal Code left in force all ordinances of the Old Regime not specifically abrogated, subsequent police prefects, searching to establish a legal basis for their arbitrary powers, cited a motley variety of precedents in legislation that seemed indirectly or inferentially to relate to prostitution.

Among these were laws penalizing the sale of obscene publications, justifying administrative steps to control "calamitous scourges," authorizing municipal surveillance of public health, and other such measures that only through violent acts of interpretation could be seen to justify the right of a civil authority to imprison prostitutes without trial.

It was essentially in this right that l'arbitraire consisted. The prefect of police, acting through his agents on the morals brigade, had the right to arrest any woman who, in his judgment, was soliciting on the street. It sufficed for him to have detected "a provocative look" or an "indecent gesture."

The arrested woman had no recourse to a court of law. Indeed, she was for all intents and purposes already placed outside the law by the very fact of her accusation. As soon as the commissaire in her quartier had written up a procès-verbal of the offense, the woman was arbitrarily subject, as a report of 1819 puts it, "to incarceration by administrative decision." Her hearing before the Bureau of Morals was a purely procedural matter.

Parent supported these policies fully, arguing that civil liberties are a privilege that prostitutes renounce when "they abandon themselves to the disorder of the passions and to all the excesses of a dissolute life". The population as a whole, he claims, approves of exceptional repressive measures to control prostitution, "whatever their severity and illegality," and the prostitutes themselves, "feeling their abjection, … realize that they cannot possibly lay claim to rights they cherish but of which they have rendered themselves unworthy". So, in Parent's mind, authority does no more than discipline and punish those whose disorderly excess it is the universally acknowledged task of government to control.

Why, then, was no law passed empowering the police to administer society's repressive will?' Parent's attempt to answer this question is one of the few occasions when he deliberately turns away from verifiable evidence and allows himself to hypothesize: the lawmakers, he surmises, "not having the documents necessary to enable them to act with full knowledge of the facts, intentionally left everything vague, thereby abandoning the repression of prostitution to the administrative authority". This is evidently an invitation to adopt Parent's own book as the heretofore lacking basis for legislation. And indeed Parent goes so far as to draw up the text of a law whose passage would remove the administration from the "false position" he considers it to be in.
_{— Charles Bernheimer: "Figures of Ill Repute: Representing Prostitution in Nineteenth-Century France", Harvard University Press: Cambridge, London, 1997. (eBook, archive.org, gBooks)}

For the laws in place at the time:
— Zacharie Clémence: "The Code d’Instruction criminelle, 1808"
— James W. Garner: "Criminal Procedure In France", Yale Law Journal Vol. 25, February, No. 4, 1916. (PDF)
— Morris Ploscowe : "Jury Trial in France" , Minnesota Law Review, (1945), 1984.
— WP: Napoleonic Code

The really curious thing is how much leeway the police indeed were given – and how arbitrarily the interpretation of legal logic applied here:

The legality of prostitution was left conveniently vague; women were, however, allowed to engage in the trade so long as they followed police regulations governing their conduct. Violation of the rules resulted in something euphemistically referred to as "administrative detention," or imprisonment without trial.

These arbitrary actions, indefensible from any legal standpoint, were nevertheless theoretically confined to women who had put themselves "outside the law" by their registration with the police.

Such theoretical limits did not hold in practice. The subjection to this system of other working-class women developed slowly but surely, expanding from a minor loophole in the regulations of the police des moeurs. The police did not get, nor did they expect, voluntary registration on the part of all prostitutes. Consequently, it was decided early in the regime that if sufficient presumption of prostitution existed, the prefecture could register a woman "by office," that is, against her will, making her subject to all the rules. From this policy there developed a necessary accompaniment, the concept of the "clandestine" prostitute, a woman who engaged in prostitution without police supervision of any sort; any woman was potentially clandestine, particularly if her conduct was "irregular."

To this mixture was added the self-expanding mandate of the police des moeurs. This creeping bureaucracy was founded on the basis of a few apparently trivial administrative decisions, with the modest ambition of ensuring that all registered prostitutes reported for their medical examinations. It ended as an administrative department with a budget of over 100,000 francs a year and a self-defined mission of purging society of its impure elements. "The police do not have a social mission of public moral reform," one of their critics reminded them at the end of the century. But by then it was too late.

By the late 1800s there had developed a virtual mania over prostitution. Arrests in Paris alone numbered in the thousands every year.
_{— Jill Harsin: "Policing Prostitution in Nineteenth-Century Paris", Princeton University Press, 1985.}

Note that within the story the police is found to have overstepped the line, somewhat!

The quoted laws:

The matter to which you refer is one connected with the municipal police. According to the terms of articles nine, eleven, fifteen, and sixty-six of the code of criminal examination, I am the judge.
[In the French original it is: Le fait dont vous parlez est un fait de police municipale. Aux termes des articles neuf, onze, quinze et soixante-six du code d’instruction criminelle, j’en suis juge. J’ordonne que cette femme soit mise en liberté.]

In the real law books from 1808 we see:

9:
The judicial police will be exercised under the authority of the imperial courts, and according to the distinctions that will be established: By the country guards and the forest rangers, By the police commissioners, By mayors and deputy mayors, By the imperial prosecutors and their substitutes, By Justices of the Peace, By gendarmerie officers, By the Commissioners-General of Police, And by the examining magistrates.

11:
The police commissioners, and in municipalities where there are none, the mayors, or in their absence, the deputy mayors, will look for police contraventions, even those under the special surveillance of the forest and countryside guards, against which they will compete and even prevent.

They will receive the reports, denunciations and complaints, which will be related to police contraventions.

They shall record in the reports they draw up for this purpose, the nature and circumstances of the contraventions, the time and place where they were committed, and the evidence or clues to be used by those presumed guilty.

15:
The mayors or deputy mayors shall hand over to the officer by whom the public prosecutor's office at the police court will be filled, all documents and information, within three days at the latest, including the one in which they have acknowledged the fact on which they have proceeded.

66:
The plaintiffs shall not be deemed to be civil parties unless they formally declare so, either by the complaint or by a subsequent act; or if they do not, by one or the other, make a claim for damages, they may withdraw within twenty-four hours; in the event of withdrawal, they shall not be liable for costs since it was served, without prejudice, however, to the damages of the defendants, if any.

The seems a bit strange for the case of "66"? Well, let's look at 166:

Article 166

The mayors of the communes, not being the chief town of a canton, will know, concurrently with the justices of the peace, of contraventions committed within the extent of their commune, by persons caught in flagrante delicto, or by persons who reside in the commune or who are present there when the witnesses are also resident or present there, and when the claimant party will conclude for his damages and interests to a determined sum, which will not exceed that of 15 fr.

They will never be able to know of contraventions attributed exclusively to justices of the peace by article 139, nor of any of the matters, knowledge of which is attributed to justices of the peace considered as civil judges.

Article 167

The public prosecutor's office will be exercised with the mayor, in police matters, by the deputy; in the absence of the deputy, or when the deputy replaces the mayor as police judge, the public prosecutor's office will be exercised by a member of the municipal council, who will be appointed for a full year by the imperial prosecutor for this purpose.
_{— "Code D’instruction Criminelle De 1808",Texte publié dans « Le moniteur universel » (en plusieurs livraisons, à partir du 18 novembre 1808) (own translation)}

While these excerpts of legalese may seem a little incongruent to their impact on the story, there is also 'an actual eyewitness account' of such a scene, said to have taken place in 1841:

It was on the 9th of January. […] He went along the Rue Taitbout, […] He was thus waiting, like an orderly on duty, when he saw a young man, well and stylishly dressed, stoop and pick up a great handful of snow, and put it down the back of a woman of the streets who stood at the corner of the boulevard in a low-necked dress. The woman uttered a piercing shriek, fell upon the dandy, and struck him. The young man returned the blow, the woman responded, and the battle went on in a crescendo, so vigorously and to such extremities that the police hastened to the spot.

They seized hold of the woman and did not touch the man. Seeing the police laying hands upon her, the unfortunate woman struggled with them. But when she was securely seized she manifested the deepest grief. While two policemen were pushing her along, each holding one of her she

"I have done no I assure arms, shouted, harm, you! It is the gentleman who interfered with me. I am not guilty ; I implore you leave me alone ! I have done no harm, really, really!"

" Come, move on ; you will have six months for this business."

The poor woman at these words,

" You will have six months for this business,"

once more began to defend her conduct, and redoubled her supplications and entreaties.
The policemen, not much moved by her tears, dragged her to a police-station in the Rue Chauchat, at the back of the Opera.

This excerpt is from the alleged witness of that scene: Victor Hugo himself.

— Victor Hugo: "Things Seen", Colonial Press: New York, Boston, (no date given), archive.org, chapter "Origin of Fantine" p42–47. Since it is of interest for OP of this question, in the original French Choses vue It says: "Elle en a pour ses six mois de prison."