Depends what you order. Electricals tend not to be allowed to be shipped from UK to other EU destinations, IME, and anything Kindle related seems to be banned cross-border. Ah the wonders of EU integration! 😉
I’ve ordered books, CDs and DVDs/Bluray from the UK site and they shipped OK to Germany, so I’d imagine France would be fine. But as above, half the time they actually ship from Germany (even the English version of books), and sometimes they give a courier shipping thing starting from Aachen airport. And sometimes I’ve had a single order (consisting only of UK English books) split into multiple deliveries all starting from different Amazon depots.