The treaty of Tordesillas granted no rights of colonisation to the French and with the rivalry that grew between the powers of France under Francis I and Hapsburg dominions under Charles V, France attempted to explore and colonise where it could. The French king is even quoted as saying of the treaty "Show me the will of Adam!".
French exploration began in 1530 with Jacques Cartier sailing to OTL Hokkaido, Japan and the Kuril Islands. These he proclaimed as Francia Novia and claimed for Francis I.
He established Francesca on his first voyage and La Perouse on his second.
Other settlements at Brest Nouveau and Plaisance followed by 1550.
Whaling and fur trade prospects made the lands of interest to the French.
The colony managed to establish mostly positive relations with the native Ainu, who were currently more angered by the Japanese incursions in the south of Hokkaido.
In 1544 the French also spread north, taking over the ailing colony of Henricia, long abandoned by most English colonists for lack of funding and supplies.