I saw several threads on that topic, with a more successfull colony, I wanted to explore that way.
Here's a brief outline I wrote months ago:
1524
Verrazano explores Chesapeake bay before heading north where he suffers damages that force him to winter at the site of New Angoulesme on the island of Manhatta [POD].
1530's
Jacques Cartier, on service of François I, explores Saint-Laurent Gulf and valley, trying to find a passage to China.
1541/1542
Due to luckier timetable, Sieur de Roberval, on king's service, arrives in time to meet Cartier before his departure [2nd POD]. With intel shared, Roberval is able to establish a colony on the site of Charlesbourg which will become Québec later.
early 1560s
Admiral de Coligny has a colony established by Protestant refugees at New Angoulesme, far south to Canada to escape the takeover of the colony of Canada by royal authorities.
1560s-1580s
The wars of religion in France have consequences as far as North America where the Protestant ruled colony of New Angoulesme and the loyalists in Saint-Laurent Valley and Acadia fight each other. Aside of a few naval raids, this is mainly a war of proxy with New Angoulesme and its Iroquoian allies fighting Hurons and Algonquins. Without being especially adamant on religion, northern colonies fight mainly by loyalism for the king while the population of New Angoulesme, being made of refugees from wartorn France, is more prone to make it a subject of discord. Finally, both side come to terms as King Henri III and Henri de Navarre ally in 1589. The ceasefire survives the assassination of Henri III.
1590s
The fragile peace between New Angoulesme and New France is nonetheless marked by continued fights between Amerindian tribes which refuse to abide by the ceasefire. The status of New Angoulesme is settled by Henri IV which makes it a separate colony from New France.
As religion wars have ceased in mainland France, the flow of settlers slows down as well, ending three decades of boom.
1610s
Samuel de Champlain, explores the course of the Mississippi all the way from the Great Lakes to the delta and claims the region for France and names it Louisiana for the young king Louis XIII.
1630s
Under Richelieu impulsion, settlement of Ohio valley begins for tobacco cultivation and the port of Richelieu (New Orleans) is built to provide an outlet on the Gulf of Mexico. However, the initiative gets soon into trouble as France enters the Thirty Years War to support German Protestant princes and collides with France, leading Spaniards to raid and burn Richelieu.