A deeper explanation as to why the Red Flag became a symbol of revolution, from http://www.crwflags.com/fotw/flags/fr_revol.html#red, which got its information from M. Pastoureau in his book Les emblèmes de la France:
In July 1791, King Louis XVI and the Royal Family attempted to flee France, dressed as ordinary people. They were arrested in Varennes, on their way to Germany. It is often said that the son of the post house's owner recognized the king after a coin. Others said that the royal princesses were recognized because they were not able to walk correctly without a servant to assist them. Betrayal might be a more rational explanation.
The king was brought back to Paris. A "Republican petition" requiring the overthrowing the king was deposed on Champ-de-Mars, where the Fête de la Fédération had been celebrated on 14 July 1790.
A lot of people gathered to sign the petition. On 17 July, when the meeting turned into a riot, the Mayor of Paris, Bailly, ordered the hoisting of the red flag, which meant at that time that the mob should disperse. The National Guards shot without warning. More than 50 rioters were killed, and were immediately considered as the first martyrs of the Revolution. The red flag, "shed with the martyrs' blood" became the symbol of the Revolution by a weird inversion of its initial symbolism.
The Blue and Red parts of the French tricolor originates in the Flag of Paris.