The Portuguese really wanted to maintain their monopoly over Brazil, so eventually there would be some sort of conflict. However, well fortifying Villegagnon island and maintaining friendly relationships with the local Indians could get the French to drive off the Portuguese attack for a long enough, until their home government reaches a diplomatic settlement with Portugal. At this point though, the future French colony in Rio de Janeiro is surrounded by Portugal as the Captaincies of Pernambuco and Sao Vincente have been successfully established to its north and south, so it remains militarily vulnerable unless the French snatch more Portuguese land. A Portuguese-Spanish union ITTL where Spain has the same disinterest in Portuguese colonies as OTL might see chunks of OTL's Brazil sold or given up to France.
To survive the initial hurdle of establishing itself, the colony will need to make money. Exporting brazilwood could turn a profit initially. Sugarcane is also an obvious economic resource, but unlike the Portuguese the French in the 16th century have not had much experience growing sugarcane, running plantation economies, or exporting African slaves so while French Brazil might end up being a giant Haiti, it would take a long time. As Rio currently is a majority European state, it's also possible that unlike in Haiti a large European settler population will come to the colony and establish a European majority. Every time French Brazil comes up someone suggest making it a penal colony for Huguenots, but the loyalty of said colony to the crown is doubtful-though once again, being surrounded by the Portuguese could cure thoughts of rebellion. Given the high level of European settlement, perhaps European colonists will survive at rates high enough to provide a labor force so maybe Huguenots indentured in the French wars of religion could provide labor in the sugarcane fields, at least for a while.
Inland from Rio is Minas Gerais, with its rich deposits of gold. If France holds on to its colony long enough to explore inland, they will definitely get a great return on investment in the form of a giant gold rush that will probably finance a lot of military adventurism back in Europe.
