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As for the symbolism of the white color, Wikipedia has a couple of explanations :
White had long featured prominently on French flags and is described as the "ancient French colour" by Lafayette. White was added to the "revolutionary" colors of the militia c**kade to "nationalise" the design, thus creating the tricolour c**kade.
And also
The colours of the French flag may also represent the three main estates of the Ancien RΓ©gime (the clergy: white, the nobility: red and the bourgeoisie: blue).
If you understand French, the article about the Drapeau de la France has a much more thourough explanation about how the tricolour prevailed.
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According to Pastoureau (probably the best expert of both history of colours and heraldry), the tricolour was inspired primarily by the American colours (not by the colours of Paris as those were red and brown), and got in competition as a revolutionary emblem with the red flag which came to represent the people against the government (on the 17th of July 1791, 50 people were killed by the national guard on the Champs de Mars after red flags were raised by the governments in order to ban manifestations).
In February 1848, insurgents brandished red flags in front of the Hotel de Ville and asked for it to become the only emblem of the Republic, as the symbol of people's misery and of rupture with the past.
But Lamartine, member of the provisional government, saved the tricolour by remarking that "The red flag is a flag of terror which is known only around the Champ-de-Mars, whereas the tricolour flag is known all over the world along with the name, the glory and the liberty of our homeland".
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I understand that Blue and Red were taken for the national flag since these colors, being a symbol of Paris, had been used by the citizens during the storm of the Bastille
In fact, this is likely to be a misunderstanding. As explained in the research of Michel Pastoureau, blue and red where not strongly associated with the colors of Paris at the outset of the French Revolution. The most likely explanation is that red and blue come from the colors of the uniforms of the Garde Nationale, that these colors were chosen by Lafayette, its first commanding officer, and that Lafayette chose them because he associated them with the American flag, then strongly associated (especially in his mind) with the idea of liberty. In turn, these colors show up on the American flag because they are on the Great Britain flag, where the red is the red cross of Saint George and the blue is the saltire of Saint Andrews, the respective Saint Patrons of England and Scotland.
So quite ironically, it seems that the French Flag owes its colors to Great Britain, France's traditional most bitter enemy.