During my year of study in Paris, I did not notice anyone who could tell I wasn't French. Maybe you could use a phonetics coach.
When the group toured France, I was the one required to interface with the hotel clerk, with the subway ticket vendor, with the waiter since nobody else had any French at all. There was no trouble in Paris or anywhere else understanding my Bavarian accent. I had no trouble understanding the workmen (and professionals) at 3 AM in Les Halles, they had no trouble understanding us. Never saw the famed haughtiness.