I find it difficult not to happen for the simple fact that the colony's economy, or at least the largest economy, will be cash croops. This economy demands a high rate of labor, more than OTL Brazil due to a greater diversity of products. Not just sugar, but also coffee, tobacco and other products. The economy will be more developed with the immigration of Jews and Huguenots, but even so, what will generate money for the crown will be Cash croops. So unless the crown wants to pay big money to other European powers. Ideally, France would have a colony or trading posts to buy not only slaves but also products such as ivory and in exchange sell weapons, steel, among other things. This pushes France towards Africa, and even if the crown itself did not want to enter. The colony and merchants will advance on the continent looking for smaller markets not controlled by Europeans. Or simply attack weaker powers like the Swedes and take over their trade colonies.well, according to the map, we already know that france has a small presence in north america, but for africa, apart from a few accounts, I don't think we'll see a large french presence.
Weck this could be the economy of the Northeast after the discovery of gold (It doesn't have the economic power of sugar production but at least it would help bring some form of economy back to the region.). Control the African coast and protect Antarctic merchants. It is the region of the colony closest to the African continent. And in OTL Ship production during this era primarily took place in coastal cities such as Salvador, Rio de Janeiro, and Recife. These cities had access to timber resources and were strategically located for maritime activities. With the crown (the portuguese one) granting licenses to shipbuilders and encouraging the establishment of shipyards and the construction of vessels. Local timber, especially the dense and durable species found in the Brazilian rainforest, such as jacaranda, cedar, and brazilwood, were the most used for shipbuilding. These woods were known for their resistance to marine organisms and provided sturdy and reliable vessels.
The shipbuilding industryl contributed to the growth of local economies by generating employment opportunities for shipbuilders, carpenters, blacksmiths, and other skilled craftsmen. It also stimulated the development of related industries, such as timber harvesting, sailmaking, rope production, and ironworks. If the sector really grows in the northeast (well, it won't be everywhere, only in coastal cities with good ports like Recife and Salvador). But at the same time in OTL the Portuguese imposed a lot of restrictions on shipbuilding in the colony. The intention was to maintain control over the colonial economy and prevent competition with the shipbuilding industry in Portugal. This policy limited the size and complexity of ships that could be built in Brazil, with larger vessels often being constructed in Portuguese shipyards. So if this restriction occurs in the French colony, the economy will remain the same in the OTL. Now if this restriction does not occur, well the sky is the limit for ship production.