Man-of-the-match Jonathan Sexton added two penalties after the interval before a Jeremy Sinzelle's score gave Stade some hope.
But replacement Cian Healy's try two minutes from time sealed Leinster's fourth European trophy in five seasons.
However there is little time for Leinster to celebrate as they now prepare to take on Ulster's in the RaboDirect PRO12 final on Saturday.
The RaboDirect PRO12 final will also be Schmidt's last game in charge of Leinster before he takes the reins at Ireland, and the head coach is eyeing the perfect send off.
"It's a trophy we have wanted for the last two months," said Schmidt.
"This is our third European trophy in three years and if you had said that at the start of the season I would have taken it with both hands.
"We have one match to play so we have to turn around and try and do our best next Saturday.
"I am a reasonably simple person, I just want to focus on next Saturday now. It is something that has eluded us in the last two seasons, we have won Europe and lost the Celtic League.
"To win the PRO12 would be massive. We will be looking to double up if we can."
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