Veteran outside-half Alain Penaud got the Parisians on their way inside seven minutes. David Skrela grabbed the second after 24 minutes.
Juan Martin Hernandez added a third try before hooker Benjamin Kayser secured the bonus point and a 24-3 half-time lead.
Replacement Yohan Montes crashed over after 59 and 71 minutes before Pierre Rabadan was shoved over by the full weight of Stade’s pack to round off an emphatic display.
: Tries: Penaud, Skrela, Martin Hernandez, Kayser, Montes 3. Cons: Skrela 2, Martin Hernandez 3.
: Martin Hernandez, Corleto, Skrela, Messina, Dominici, Penaud, Fillol, Marconnet, Kayser, De Villiers, Auradou, M. James, Rabadan, Martin, Sowerby.
: Sarramea for Skrela (47), M. Bergamasco for Penaud (60), Williams for Fillol (48), Blin for Kayser (56), Montes for De Villiers (56), Marchois for M. James (63), Parisse for Martin (28).
: Tries: M. Jones. Cons: M. Jones. Pens: Connor.
: Cashmore, Terblanche, S. Parker, L. Davies, Mustoe, Connor, Rees, D. Jones, Hibbard, A. Jones, Newman, Bateman, Bater, Beech, Thomas.
: A. Bishop for L. Davies (51), M. Jones for Connor (64), Wells for Rees (55), Millward for D. Jones (77), Bennett for Hibbard (67), Tandy for Bateman (15). Not Used: Griffiths. Att: 10,700
: Chris White (RFU).