The northerners' chances of qualifying for the quarter final stages for the first time since they lifted the trophy back in 1999, were dealt a cutting blow as Stade hooker and skipper Mathieu Blin, number eight Shaun Sowerby and right wing Mirco Bergamasco all touched down in a power-packed second half display at Stade Jean Bouin.
Italian international Bergamasco and Brian Liebenberg both missed chances to cross in a first half which was edged by the home side, 9-3. Fly-half David Skrela kicked three penalties from five attempts, to Humphreys' sole effort on 23 minutes.
Close range mauls on the restart saw the Stade pack impress, and Blin (43 minutes) and Sowerby (56) were easily rolled over in front of 11,628.
Skrela converted both before Bergamasco (65) was set up for a run to the right corner after Liebenberg's initial incision.
A Kevin Maggs break enabled Humphreys to dangle a crossfield kick to the left corner for 20-year-old Bowe to leap impressively to collect for a well-engineered reply on 69 minutes.
Humphreys converted to boost his Cup points tally for the season to 39, but despite a gutsy performance, Ulster thoughts were turning to next Saturday's must-win return tie at Ravenhill (kick-off 1.00pm).
Having taken just four points from the opening three rounds, Ulster coach Mark McCall is banking on their improving home form.
"We're determined to win our home games and pick up an away win at the Cardiff Blues to move up the table a bit," he said.
"We played well in the final 20 to 25 minutes today, and we'll take something out of that.
"We simply couldn't get our hands on enough ball. We knew they had a good defensive lineout and we didn't combat it well enough.
"A lot of the younger players showed up well when we were on attack in the final quarter," added former Ireland centre McCall.
"I thought the back three of Tommy Bowe, Bryn Cunningham and Jonathan Bell played well when we got some ball in the final minutes."
Pool 6:Stade Francais 30 ULSTER 10, Stade Jean BouinScorers: Stade: Tries: Blin, Sowerby, Bergamasco; Cons: Skrela 3; Pens: Skrela 3 Ulster: Try: Bowe; Con: Humphreys; Pen: Humphreys
(15) Bryn Cunningham(14) Scott Young(13) Jonny Bell(12) Kevin Maggs(11) Tommy Bowe(10) David Humphreys(9) Kieran Campbell(1) Ronan McCormack(2) Paul Shields(3) Rod Moore(4) Rowan Frost(5) Matt McCullough(6) Campbell Feather (Capt)(7) Neil Best(8) Roger Wilson
Replacements used: Gary Longwell for Frost (ht), Nigel Brady for Shields (68), Neil Doak for Campbell (75). Not used: Bryan Young, Tim Barker, Adam Larkin.