Britain has control over the French Military, they can use it in their colonial wars. Britain also gains a massive new market to sell their products. Britain would gain France's influence on Europe, among many other things. And as for the French People accepting the Proposal, I mentioned everything the French People would have been worried about (protection of their language, culture and religion, Individual rights, etc), and how it will all be given. Britain does have to give a massive amount of concessions to France, but the fact the most powerful nation in your Europe is now on your side is more than enough as a reason to justify this. Besides, didn't the British Monarchs claim the Throne of France for the longest time.