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The away side made a good start to the game, securing their first try after just eight minutes as James Haskell was able to create space with a solid midfield break.
The French outfit clawed six points back thanks to two penalties by Jules Plisson in the first half, but Wasps ended the first period with a substantial lead thanks to a penalty by Goode.
The second half saw Stade Francais crumble, as Haskell's offload in the 62nd minute found Ashley Johnson, who subsequently powered over, and with just three minutes of the game remaining, Goode's penalty finished the game off.
The result means that the High Wycombe outfit will take part in next season's Champions Cup.