The association with saints is probably correct. Red and blue were indeed respectively the colours of Saint Denis and Saint Martin.
The early history of the French flag is lost in obscurity, and it is not always easy to trace the various modifications that it has undergone. At the earliest date of which we have record we find the kings of the Franks marshaling their forces under the plain blue flag known as the Chape de St. Martin. Later on the red flag of St. Denis, known as the oriflamme, came into use, and was held in great popular esteem, until by the tenth century we find it accepted as the national flag.
- Hulme, Frederick Edward. The Flags of the World: Their History, Blazonry and Associations. Library of Alexandria, 1897.
Blue was long associated with Saint Martin. The ancient battle standard of France was (supposedly) the blue cope of Saint Martin, famously said to have been divided with a freezing beggar. Though known as the chape de saint-Martin, it likely wasn't so much clothing as it was the banner of his abbey. It might have been blue because that (and green) was the colour of confessors.
The ancient kings of France bore Saint Martin's blue hood or cap for their standard for six hundred years.
- Preble, George. Our Flag: Origin and Progress of the Flag of the United States of America. Albany: Jnel Munsell, 1872.
Red was similarly associated with Saint Denis. The flag of his abbey was a banner made of red silk, known as the oriflamme. During the High Middle Ages, this red flag superseded St. Martin's blue cope as the standard of the French Kings. Sources differ on what the banner looked like exactly (e.g., plain vs adorned), but it is agreed to be (more or less) a red banner.
The first half of the twelfth century witnessed a solidification of the alliance between the abbey (and her protector Denis) and the Capetian kings. In the twelfth century the Capetians began the practice of retrieving from St.-Denis their war banner, which came to be identified as the oriflamme of Charlemagne.
- Gaposchkin, Marianne Cecilia. The Making of Saint Louis: Kingship, Sanctity, and Crusade in the Later Middle Ages. Cornell University Press, 2008.
Given their long tradition as national symbols, this seems quite plausible as an explanation for the Parisian livery colours. Charles VII later adopted the more familiarly coloured cornette blanche.