Just to make sure I'm not completely imagining things I checked the french dub and voilà, he pronounces his name PiKAHr.
So a family emigrated to England, started pronouncing their name PiKAHD and after some generations moved back to France?
And it's not the casting choice I have a problem with. I love Patrick Stewart and I love him as Picard. I just wish someone had taught him some basic french.
Following the reunification of 2112, when Britan's continental holdings were restored to the Crown, many former French subjects began to learn English. By Picards time the United Kingdom of Great Britain and France was mostly English speaking.
You might think you're joking, but check out the 1940 proposals for a union between France and the UK in face of the Nazi German invasion of the former.
And of course, the British royal family is descended from the French royoals. Up until about 1600, the monarch's full title included a claim to the throne of France as well, and I think France got priority (ie, 'King of France and England,' not the other way round... Richard the Lionheart certainly thought France was the more important bit...)