The head of the French teaching "team" I had in grad school was from France, yet she spoke nearly perfectly "unaccented" American English. (As you already know, the hard "r" sound is especially difficult for native French speakers to master.) We had routine spoken exams with each member of the team; when I rotated 'round to her, I commented (En Français, s'il vous plaît!) that her American accent appeared flawless. She actually
blushed.