The Pretoria outfit secured a bonus-point victory in their Pool 4 opener, running in eight tries against a reshuffled Parisian outfit.
Young wing Cheswill Jooste starred with a hat-trick, while fly-half Handre Pollard controlled the game and converted the majority of the tries, adding 16 points to the total.
The Bulls got off to a blistering start with Jooste finishing an early move to open the scoring inside the first minute, with Pollard adding the extras.
Cobus Wiese and Cameron Hanekom crossed before half-time as the home side built a solid 21-6 lead at the break.
Stade Francais responded well after half-time, with Jacques Botha and Petero Mailulu scoring tries, both converted, to briefly narrow the gap and show the visitors were still competitive.
However, the Bulls' power and pace proved decisive in the final quarter. Marco van Staden, replacement Jeandre Rudolph and hooker Jan-Hendrik Wessels added further tries.
Jooste then sealed his hat-trick with two late scores in quick succession as the Parisian defence tired, while Pollard's accurate kicking kept the scoreboard ticking over throughout.