Bolton Wanderers striker Nicolas Anelka put the French into a seventh-minute lead, with Henry doubling the advantage seconds later to draw level with Michel Platini's record of 41 goals for his country.
Karim Benzema's double, Jerome Rothen's finely executed free-kick and Hatem Ben Arfa's late strike completed the scoring in a match that wild weather had done its best to disrupt.
Desperate conditions in this far flung atlantic outpost threatened to postpone the game. Unable to land as scheduled on Friday, Raymond Domenech's side were forced to spend the night in the Norwegian coastal city of Bergen.
They finally made it to Torshavn with four hours to spare, but both sides agreed the fixture should go ahead as planned. "Eleven hours in an airplane with stop-overs in Scotland and then Norway is not ideal for anyone, but my players are taking it in their stride," Domenech said upon arrival, and so it proved on the pitch.
This scoreline came as a welcome change for the French attack, which had proved impotent in its last two matches against Scotland and Italy. In front of a crowd of barely 1,500 fans in this tiny stadium bordered by a roundabout, a swimming pool and a carpark, Anelka eased Gallic nerves with his early contribution.
Then came Henry's history making moment, a right-footed shot past Faroe Island keeper Jekup Mikkelson. Four minutes into the second half and Benzema got the first of his two goals before Rothen, playing for his country for the first time since November 2005, curled in a sweetly taken free-kick.
Benzema made it 5-0 in the 79th minute with substitute Ben Arfa celebrating his first international cap with France's sixth in the second minute of injury time.
France's win lifted them up a place into the runners-up berth in Group B on 22 points, two behind Scotland. Third-placed Italy can regain second if they beat Georgia later on Saturday.