Blue is for Saint Martin.  He was a gallo-roman officer that helped the poor.  A poor person was freezing in the snow, so Saint Martin gave him his coat.  History tells us that he used his sword to rip of his coat.

White is the color of the Virgin Mary and Joan of Arc.  It is also the color of royalty.

Red is for Saint Denis.  He was the patron saint of Paris.  He protected France.