The 2011 finalists ran in six tries to overtake Grenoble at the top of the table to clock their 17th win in their last 19 home games in the tournament.
The Exiles took the lead with a third-minute penalty from scrum-half Alex Davies, but found themselves trailing 18-3 at the break after the home side ran in three tries. The bonus point was clinched six minutes into the second half with a penalty try.
The visitors conceded one try at the end of the first-half when number eight Alfie To'oala was in the sin bin and then two at the start of the second period when fellow back-row man Lee Beach also saw yellow.
But the Exiles rallied to score two tries in the space of five minutes by right wing Phil Mackenzie, both converted by Davies, to cut the gap to 15 points midway through the second half.
In the end, though, Stade Francais wrapped up the game with their fifth try from Francis Fainifo six minutes from time.