France was a longtime arch rival of Britain and, generally speaking, anything that was bad for Britain was good for France. Not only that, but France had recently lost all of their colonies in North America to Britain during the 7 Years War (French and Indian War for the US) and so they jumped at the prospect of inflicting the same kind of hurt on Britain as had been inflicted on them.

The only thing holding France back was fear of England. If France declared war and then the Americans were crushed France would be left in a very awkward position. But as the war went on and it became clear that the Americans were doing quite well France felt more confident that the war was probably winnable. At this point French support changed from subtle (supplying weapons and money to the Americans) to open; declaring war.