Short answer:

Yes, the French troops used one kind of chemical warfare in Algeria. And yes, they also used chloroform during the Siege of Laghouat. Yes, many suffered and died in relation to the application of chloroform 'at Laghouat'.
But those who suffered and died were French troops, on the operating table.
This is certain.

The claim that the French poisoned large contingents of inhabitants of that oasis with chloroform seems to be a conflationary tale.
This is a reasoned theory, explained below.

Chemical warfare by French troops in Algeria

These 'one of the first' recorded instances of chemical warfare by French colonial troops was perpetrated by colonel Pélissier, who in 1852 would participate in storming the Oasis of Laghouat.

But it was in 1845 that

1095 out of 1150 men of the Kabyl Tribe Ouled-Rhia die of suffocation in the cave of Nemchia after the French Colonel Pelissier had given the order to generate smoke by burning freshly cut wood.

— L. Szinicz: "History of chemical and biological warfare agents", Toxicology, Vol. 214, p. 167–181, 2005. (doi // Same incident listed here.)

Note that this paper mentions a few earlier uses of chemical agents in various forms. But it doesn't mention chloroform at Laghouat. Also, this would classify as a classic 'smoke-em-out'. Employed much earlier for example by Sasanid troops against Romans at Dura-Europos, or even 82–72 BC by Romans against Charakitanes. In the latter case the effects are described as "being like phosgene" (Kim Coleman: "A History of Chemical Warfare", 2005).

Earliest mention of chloroform in warfare

The earliest idea to use chloroform in war that I found was:

Also in April 1862, shortly after the naval engagement between the USS Monitor and the CSS Virginia ended in a draw, Commodore L.M. Goldsborough reported a rumor that the Confederates were going to use chloroform as a knockout gas against the USS Monitor to produce insensibility of their crew. A similar suggestion was made by Joseph Lott from Hartford, Connecticut in 1862 to load hand pumped fire engines with chloroform and spray it on the enemy troops behind their earthworks defending Yorktown, Virginia, and Corinth, Mississippi.

— James A. Romano & Jr. Brian J. Lukey & Harry Salem: "Chemical Warfare Agents. Chemistry, Pharmacology, Toxicology, and Therapeutics", CRC Press: Boca Raton, London, ²2008.

That conflict is known for a lot of similar plans of using various acids and poison gases on enemy troops. (Coleman)

Chloroform was 'probably the second most suggested chemical agent then'. But:

The concept, although, appeared “impracticable, as it seems to us that the vapor of chloroform would not be sufficiently concentrated.”

— Guy R. Hasegawa: "Proposals for Chemical Weapons during the American Civil War", Military Medicine, Volume 173, Issue 5, May 2008, p. 499–506. doi

The conflation unfolds

Most treatises on the history of chemical warfare leave out even the 1845 incident, none mentioned Laghouat in 1852. So what is happening here?

The one blog example given in question is indeed helpful.

Moreover, these same specialists [historians] evoke the use, for the first time, of chemical weapons, a kind of chloroform that disintegrates everything in its path.

Testimonies of this hecatomb were written in black and white by officers of the French occupation army and by a painter, Eugène Fromentin, who put together his correspondence in a book entitled "Un été dans le Sahara" (A Summer in the Sahara), which recounts the state of the town on his arrival, a few months after the massacre, and which includes details of the massacre recounted by a lieutenant.

— 'Babzman': "Massacre et génocide à Laghouat, le 4 décembre 1852".

This is interesting for indeed two reasons:

1. Chloroform is not only a knock-out gas. In small amounts it will put people to sleep, in larger amounts it would kill. But if left in the open, hot, oxygene and sunlight rich environment, it will degrade to phosgene, an indeed deadly poison gas and 'classic' chemical warfare agent.

2. This blog depiction gives a source. The French painter Fromentin did go to Algeria, visited Laghouat, and described the after effects and some eyewitness accounts of a really gruesome massacre.
   As the blog entry itself shows: he doesn't mention any gases used. Full book on archive.org. This quoting of his reference material does not support the chemical warfare allegations for this, nor does the full book. Source, quote and claim just do not match. In this case, they seem deceitful.

Positive evidence in shady lights

This is then the result for me always when looking for a confirmed use of chemical warfare at Laghouat: there is none retrievable. This might mean little, as 'not everything is on the net', if it is perhaps behind a paywall, or I may be just a bad researcher. Wikipedia entries don't count much, especially not when not referenced. The genealogy wiki excerpt however claims that Ernest Adrien Liebert would have given testimonial to their use.

As I cannot confirm this in any way, this I also categorise into 'unreferenced claim, therefore doubtful'.

Even more so: The genealogy wiki cites as their source a book by 'Hadj Mahmoud Kazi', which has left some traces here, and the siege events again here. The text on that wiki claims that it was taken from that book. The excerpts from that book on the blog website appear to be missing the chloroform detail. The chloroform details are presented on another page, but this time the connection to Liebert is completely missing.

Any real book like that then eludes my searches. But notice that the author has a speaking name: a devout pilgrim, named after the prophet with a family name meaning 'judge' I acknowledge that Arabic-Latin transliterations are just a nightmare. If that book is available on the net or via net-searches, but only in Arabic, then this means someone with better language skills might have to unearth it.

It is still noteworthy that an alleged testimonial supposedly from a French source seems only be traceable through Arabic authors. 'Innovative use of weapons' should have left more traces in French language sources?

Chloroform warfare and battlefield characteristics

Since the use of chloroform as a direct warfare agent seems dubious: rather fresh invention, untested, in the open you'd need large canisters/lots of grenades, in a desert trek of relatively small colonial troops, this looks like logistics nightmare.

Chloroform was also used in large quantities for surgeries in the Crimean War — and sometimes this is credited with 'first mass use'. But the French tried during the First World War to use chloroform as an active agent doubling as a solvent. But even then the results were unsatisfactory, because the gas was just deemed to be too volatile (de:WP, sadly also unreferenced).

But we still do see an account of an eyewitness from his memoirs about the use of chloroform at Laghouat. Only to be used on French troops when going into surgery as a new anesthetic.

On December 21, the doctors came to tell me that after consulting each other, they had decided to amputate General Bouscaren, whose leg was gangrenous. As he had had a light meal, they waited until evening. The chloroform they used was probably of poor quality, for it was very difficult to put him to sleep; he talked, sang, gesticulated, while keeping his hand on my sleeve, for he had demanded that I be there. […]

He was buried in the new cemetery which had just been inaugurated and where new crosses were planted every morning. In front of the entire garrison under arms, in the name of France, I bid a supreme farewell to this hero, whom General Pélissier, in a patriotic and touching agenda, called a valiant knight. I also attribute to this poor quality of the chloroform used the death of almost all our great wounded.

— François Charles du Barail: "Mes souvenirs", 1897. (archive.org)

Summary

Too much about using 'chlorofom bombs at Laghouat' doesn't add up. Unless sources like Liebert can be reliably confirmed, this looks much like a conflation that gets copied down the whisper chain?