It is not named after the French province of Maine. In fact, the French called the area "Acadia". When the Area came under English control, Sir Fernando Gorges named the land "New Somerset" which was greatly disliked by King Charles.

In 1639 the King responded in a charter that the area should "forever hereafter be called and named the Province or County of Mayne and not by any other name or names whatsoever." So from Mayne we get Maine. The fact that the state shares a name with a French Province is coincidence.

you can read more here: http://www.maine.gov/msl/maine/meorigin.htm