Another Restoration War most likely. Still got bad memories of the earlier French occupation from 1795-1803.
But the French might be able to keep the place if they play their cards right. You need a governor willing to work with and coopt both the northern elites of El Cibao and the cattle barons near Santo Domingo. The former are easy, as theyre mostly merchants who want business and a state willing to help and invest in them. The southerners... Well, thats hard. They want patronage and money, preferably in increasingly higher amounts. And arent keep to government centralization.
Furthermore there must be AN ABSOLUTE GUARANTEE that slavery will remain banned and that mulattos can keep the privileges of citizenship they had. Would be great if the French offer French citizenship to all men on the island but I dunno the plausibility of that.
All this said, its much easier to have the French keep Eastern Hispaniola during the original cessation in 1795. You'd only need to change a few policy decisions and the governor.
In all cases that France manages to keep Santo Domingo I forsee the French using the country as a staging point for various interventions in Latin America, a naval base in Samana, and creating greater animosity with Haiti.