Napoleonic France - self aggrandazing propaganda crap term, in the same vein of "Freedom fries" or Americo Vespucci's "look guys, I am the first person to ever figure out America was a different country" (note: lol, no). Napoleon III coined the term in order to claim "historical rights" over Spanish and Portugese colonies, mainly during the whole Maximilian affair (see guys? We also contributed to colonize America too, just like you! Now let me install a puppet regime in Mexico plz), and the term catched on because of the huge world wide influence of France during that historical period.
I frankly dislike that term, for it is quite inaccurate and semantically wrong: following that logic, Canada and New Orleans would be also part of "Latin America", not to mention that the idea of equating the French cultural influence over the region at the same level of Spain and Portugal or even Italy and Englad (just compare the size of Jamaica with the French Guiana); is laughable.