Cardiff are second in the URC and have three important derbies over the festive period, which influenced coach Cornel van Zyl’s decision to change his squad after the win at Zebre.
Three players made debuts, with lively full-back Young making the debut, while center Elijah Evans and scrum-half Euan Davis came off the bench.
Cardiff were also boosted by the return of winger Stephens and physical back Mason Grady continued his return on the other flank after starting in Parma.
Down the stretch, fly-half Ian Lloyd was forced off in the first half with an injury to his right shoulder.
Cardiff’s performance against Ulster at the Arms Park next Saturday is likely to shape their outlook for the third and fourth rounds in January given their URC play-off push.
Stade, fourth in the top 14, were twice stopped on the line before full-back Mathis Ebo opened the scoring in the 16th minute with a smart finish down the right following a line break by hooker Giacomo Nicotera.
The try-scorer converted the try-saver with a superb effort to deny scrum-half Ellis Bevan while Cardiff were in possession on the line.
Home tight-head prop Braxton Asi escaped without a card for a high tackle on James Botham, but Cardiff equalized thanks to a penalty in the 23rd minute.
He kicked on the 22, applied pressure and, with a brilliant assist from Young, turned the ball to the left for a fit-again Stephens to cross.
The novice full-back, whose performances may have brought Penarth RFC some joy after their clubhouse destroyed by fire Last weekend, he again went over himself for the same corner after 33 minutes when the forward attacked to create space far wide.
Cardiff had led at half-time, but trailed 17–10 after 50 minutes had passed when flanker Tanginoa Halaifonua headed into an empty hole in midfield and then Ebo dived over for his second try.
Stade were getting their bonus when scrum-half Thibaut Motassi took a quick tap and offloaded the lead to substitute forward Juan Martin Scalzo.
Cardiff made a pointless start to their campaign after forward tries by Louis Forsons-Bourdet and wing Charles Laloie were unable to connect with Sebastian’s close-range finish.