That's pretty easy. There was already a lot on animosity over Spain's push for an Indian territory between the Miss and the Appalachians. Furthermore there were conflicting views over portions of western Florida and most importantly the US saw free travel down the entire Mississippi as crucial. This included tariff free passage past New Orleans and use of warehouses at reasonable rates.
Just have Spain cut off travel down the lower Mississippi and the US will be forced to take military action. As for French and British reactions...the primary row between the US and Spain occurred in 1795 or thereabouts. That would make Republican France somewhat sympathetic to the US while Britain would probably support Spain. But at that time direct military intervention is unlikely as both of those nations had other issues.
Delay the war just Three or so years and the situation reverses. Napoleon was looking for allies after Egypt and saw Spain as far more useful than the US. (See the Quasi War with France as proof of this.) Conversely Britain coveted good relations with the US and the pre-Jefferson Federalists, especially Hamilton, were willing to consider that option in order to seize New Orleans and Florida.
Hope that helps.
Benjamin