A frozen corner at Stade Jean-Bouin meant the game began 95 minutes after the scheduled kick-off time.
Waisea Nayacalevu and Julien Arias put the French side 17-5 up at the break with Mat Luamanu crossing for Quins.
Craig Burden added a third Stade score before Marland Yarde and James Chisholm went over for late tries.
Quins knew they had to win the game to progress to the quarter-finals but the home side went through instead, and will be away to Ospreys in the last eight.
A corner of the pitch was still frozen at the scheduled 13:00 GMT start but play was able to start at 14:35.
Stade Francais: Bonneval; Sinzelle, Vuidarvuwalu, Bosman, Camara; Plisson, Genia; Zhvania, Panis, Slimani, Gabrillagues, Pape (capt), Nicolas, Lakafia, Alberts.
Replacements: Burden, Felsina, Melikidze, Pyle, Ross, Daguin, Millet, Arias.
Harlequins: Brown; Yarde, Hopper, Roberts, Visser; Swiel, Care (capt); Murphy, Buchanan, Sinckler, Merrick, Matthews, Clifford, Wallace, Luamanu.
Replacements: Gray, Evans, Jones, Ward, Chisholm, Dickson, Jackson, Alofa.
For the latest rugby union news follow @bbcrugbyunion on Twitter.

A preview showed the pair dancing to Beyonce's Single Ladies.
The clip, posted on YouTube, shows Corden arriving at the White House for a tour before Mrs Obama gets into his car.
The footage, which was recorded last month in Washington DC, will air on the British star's Late, Late Show in the US on Wednesday.
Mrs Obama is seen telling the presenter: "I hear you're here for a 1.45 tour and I had a little time on my hands so you want to go for a spin?"
The First Lady then tells Corden she "rarely" gets to listen to music in the car and the only time she has ever sat in the front passenger seat "rocking out" was when one of her daughters was learning to drive.
Other stars who have appeared on Carpool Karaoke include Adele, Sir Elton John and Stevie Wonder.
Corden began hosting The Late, Late Show in March last year.
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The 28-year-old Australian finished on 15 under par, with American Kevin Chappell his closest rival on 11 under.
Day, whose halfway total of 129 was a record for the Florida event, shot a one-under closing round of 71.
Northern Ireland's Graeme McDowell and Rory McIlroy finished at eight and seven under respectively, while England's Justin Rose was five under.
American Justin Thomas bettered his third-round 75 by 10 shots on Sunday to finish on 10 under in a tie for third. Rose also shot one of the day's best rounds, but his 66 was only good enough to move him into a tie for 19th.
Day dropped two shots on the front nine, but birdied the 10th and 12th to get back to level par for the round.
The US PGA winner also birdied the 16th after a superb chip to the green as he earned his 10th PGA Tour title.
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Harlequins were knocked out of the Challenge Cup by defeat at Top 14 side Stade Francais in a match delayed because of a frozen pitch.
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US First Lady Michelle Obama is joining James Corden in his hit sketch Carpool Karaoke this week.
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World number one Jason Day maintained his four-stroke advantage to win the Players Championship at Sawgrass.