Seems logical to me. The French helped the U.S. to gain there independence as a revenge against the British for the The French and Indian War (1756-1763). The Strategy was easy: If we can't have , neither will the English. They won this time , but this was a poisoned victory, as the treasure chests were empty and this was one one the reasons why the Revolution started in France. A second reason was the American example which largerly inspired the French revolutionaries. A thrid reason was that one of the most popular Generals was Lafayette who was a big friend of the U.S.
When Napoleon came to power, he feared that the British might want a revenge and sold Louisiana to the Americans. This would make the new U.S. ally stronger against the English, prevent the English from taking an undefended territory and allow more money to prepare the invasion of England. The invasion did not happen because the English won at Trafalgar and got control over the waves and that Napoleon had to send his army against the Russians and the Austrians at Austerlitz instead. By gainig control over the sea The English could later lauch raids against America.

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