France Antarctique was a French colony South of the Equator, established in 1555 in and around the modern state of Rio de Janeiro in modern Brazil, which came to an end in 1567 by the Portuguese.
France Équinoxiale was a French colony around the Equator, established in 1612, around the Brazillian State of Maranhão. It too fell to Portuguese arms in 1620, with São Luís, originally a French city, being repurposed as a Portuguese city.
But what if both France Antartcique and France Équinoxiale were more successful, could it have led to a larger presence in French colonialization in the Americas? What could it mean to places such as Louisiana and Quebec?
And what would the name of these countries be if they were to go independent?