The French relied on domestic sources for the most part. English oak was considered superior but became increasingly scarce throughout the 18th and 19th Century. The English used both North America and the Baltic as sources for masts. North American oak were prone to rot and was not highly prized.
Apparently North American oak got better by 1812. The Southern live oak used in American frigates was very rot resistant and Old Ironsides was practically impenetrable.