The arms of Mantes-la-Jolie.
Blazon: Mi-parti, au premier d'azur à la fleur de lys d'or, au second d'or au chêne arraché de sinople englanté du champ.
Mantes is in the Département of Yvelines which was created in 1968 when the former Département of Seine-et-Oise was split into three. Somehow Yvelines inherited the arms of the former Département unaltered. The arms are France Ancient over which two wavy bends represent the rivers Seine and Oise.
Blazon: D’azur semé de fleurs de lys d’or aux deux bandes ondées d’argent brochant sur le tout.
Heading eastwards towards Versailles the riders pass through the Commune of Saint-Cyr-l'École, where the military academy founded by Napoleon was situated from 1808-1945
Blazon: D'argent à la croix haussée d'azur semée de fleurs de lys d'or, fleurdelysée du même et sommée d'une couronne royale d'or, accostée en pointe de deux shakos de Saint-Cyrien affrontés au naturel.
The crowned cross was supposedly the badge of a school founded at Saint Cyr in 1684 by King Louis XIV at the request of his mistress Madame de Maintenon.
I note that the emblazonment here shows a suspiciously English-looking crown. The unusual charges that flank the cross are képis with shako plumes nicknamed "casoars" (the plumes were first used in 1855, the same year as cassowary birds came to Paris Zoo - though the plumes were not made of cassowarys' feathers).