The Parisians led 17-3 at the break, and raced to a 31-3 advantage early in the second half with their fourth try.
In all the French Top 14 leaders ran in six tries, with Lionel Beauxis and David Skréla kicking four and two conversions respectively. Skrela also kicked a penalty.
Former Italian international David Dal Maso weighed in with Calvisano's try, which was expanded on by a penalty and a conversion by fly-half Andrea Scanavacca.
But Dal Maso was utterly eclipsed by a man of the match performance from opposite number Sergio Parisse, the current Italian number eight shirt incumbent.
Stade Français' tries came from full-back Nani Corleto, wings Julien Saubade and Julien Arias, centre Geoffroy Messina, flanker Mauro Bergamasco, and reserve lock Radike Samo.
The scorers:
For Calvisano:
Try: Dal Maso
Con: Scanavacca
Pen: Scanavacca
For Stade Français:
Tries: Corlets, Saubade, Arias, Messina, Bergamasco, Samo
Cons: Beauxis 4, Skrela 2
Pen: Skrela
Calvisano: 15 Paolo Buso, 14 Apenise Vodo, 13 Michael Gallinetti, 12 James Downey, 11 Warren Spragg, 10 Andrea Scanavacca, 9 Paul Griffen, 8 David Dal Maso, 7 Aaron Persico, 6 Alessandro Zanni, 5 Ben Gissing, 4 Justin Purll, 3 Rod Moore, 2 Leonardo Ghiraldini, 1 Gabriel Bocca.
Replacements: 16 Giorgio Intoppa, 17 Lorenzo Cittadini, 18 Milton Ngauamo, 19 Maurizio Zaffiri, 20 Pino Patelli, 21 Cristiano Zanoletti, 22 Michael Cagnoni.
Stade Français: 15 Ignacio Corleto, 14 Julien Arias, 13 Geoffroy Messina, 12 Brian Liebenberg, 11 Julien Saubade, 10 David Skrela, 9 Alexandre Albouy, 8 Sergio Parisse, 7 Mauro Bergamasco, 6 Boela du Plooy, 5 Mike James, 4 Arnaud Marchois, 3 Pieter de Villiers, 2 Mathieu Blin, 1 Sylvain Marconnet.
Replacements: 16 Dimitri Szarzewski, 17 Yohan Montes, 18 David Auradou, 19 Radike Samo, 20 Jérôme Fillol, 21 Lionel Beauxis, 22 Juan Martin Hernandez.
Referee: Donal Courtney