Howell posted a third round score of 67 to pick up four strokes and reach six-under-par for the tournament, while Hansen's round of 70 helped him keep pace.
Marcel Siem, the halfway leader, lost his overnight advantage with a round of 73 to put him two shots back in a tie for fourth with home hope Raphael Jacquelin, with South African George Coetzee on his own in third.
The weather was again less than favourable in the French capital, and play began early to avoid predicted storms. There was a brief suspension when the thunder and lightning hit, but the round was eventually completed under dark skies.
Graeme McDowell sank a birdie putt at the last hole at the very moment the weather-horn sounded, completing a round of 71 which leaves him at one-under-par for the tournament.
He yelped with delight as it dropped, pleased to avoid what could have been a lengthy delay to finish off his round.
"That was the golfing equivalent of a buzzer beater!!!!," said McDowell afterwards on Twitter. "Ya little dancer. Tidied up a dodgy day."