We live in the US and often travel to France.
It has actually prevented us on multiple occasions from spending an extra 2-3 day family holiday in London combined with an EU trip. It won't kill us, but why spend an extra $500-700 if we don't have to? The per diem amount isn't palatable.
Assuming that the cost is indeed higher for US-France-UK-US compared to US-France-US
because of APD why don't you do US-UK-France-US.