IOTL the French supported the American revolutionaries against British and American Loyalists. It both aggravated the (already abysmal) state of their finances and proved that founding a new republic was possible in that day and time.
Could the reverse happen? Ancien régime France bankrupts itself by supporting a radical revolution in the British Isles, hoping to turn the old foe into a key ally, only to succumb itself to revolution a few years later. Meanwhile, the House of Hannover still rules British America.
Is it plausible? How can it be done?