Well, strictly speaking everyone has an accent, including native speakers. But being able to pass for a native is perfectly possible; in fact my brother can do it in France, a country that is famous for spotting foreigners a mile off.

How did he do it? He spent several years there and really worked at it (he can also do a convincing range of British accents). His one regret is that he nailed it in a somewhat bucolic part of France, so the cool Parisiennes just assume he's a paysan.

Is it harder? Yes. Impossible? Far from it. Although I'll bet you elocution lessons would help (my brother hasn't done any).