WI: Franco-American War of 1835?

Whilst doing research for an early 19th-century TL I came across this article on JSTOR: http://www.jstor.org.ezproxy.lancs.ac.uk/stable/27547532 .

The article discusses the issue of the non-payment of the 25 million francs of French reparations agree in 1831. The required appropriations were denied by the French government in 1834, which then refused to negotiate due to insulting language used by Jackson when discussing the matter with Congress. Cass suggested the issue of letters of marque to allow Americans to compensate themselves from French shipping. If one was to suppose that relations continued to deteriorate (the exact circumstances can be put down to Jackson's temper and Hanlon's Razor) then how might the war go?

If war was seen as genuinely likely then it is possible that the defense spending bill of 1835 which aimed to appropriate $3 million for fortifications of coastal settlements might go through. I don't know much about the relative strengths of French and American military at this point but I imagine that it would probably come down to threats on the American seaboard, trade, and possibly American attacks on French Caribbean colonies?
 
France had already been involved in a diplomatic spat with New Grenada involving the imprisonment of the French Consul in 1833 for which they threatened the naval bombardment of Cartagena; this continued on to 1834 and could perhaps become intertwined with the French conflict with America (at least as co-belligerents)? If France went ahead with attacking Cartegena they threatened the destruction of significant American mercantile interests perhaps providing an additional spark for the war breaking out.
 
How strong was the July monarchy in 1835? It looks like France's internal politics at the time postulated by the OP, would make a strong response difficult. The flip side, is that the US lacks the political willpower to project beyond American shores.
A conflict might look a little like this:
images
 
A conflict might look a little like this:

That was my suspicion too; I know that France mustered sufficient naval fleets to blockade Mexico in 1838 and threaten Columbia with 2,600 troops. Probably enough to annoy the Americans and defend Caribbean colonies so perhaps it would be little a 2nd Quasi-War. Would appreciate actual detail on relative strengths if anyone has them.
 
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