The win, courtesy of two tries and the superb kicking of centre Richard Dourthe, lifts the Avirons off the bottom of the table for the first time in three months.
In truth, the Parisians probably paid the price for a little complacency. Having rested for the Christmas fortnight, coach Fabien Galthié opted for a little more cotton wool treatment, and rested Remy Martin, Juan Hernandez and Pieter de Villiers.
After Dourthe and David Skrela had swapped penalties in the opemning twenty minutes, it was Skrela who got the match's first try, charging down a kick from Gerard Fraser and finishing it off hiumself, after the charge down had the good fortune to rebound into his hands. He also converted.
The fly-half, who was in terrific form in the week the French rugby public voted his Paris understudy Lionel Beauxis the most surprising omission from Bernard Laporte's Six Nations squad, made it 3-13 shortly before half-time, but two lapses in concentration saw the lead wiped out.
First Bayonne centre Sam Gerber intercepted a Mirco Bergamasco pass and went under the posts for a try, and then Rodrigo Roncero collapsed a scrum, allowing Dourthe to equalise. Roncero saw yellow for the incident, as did Bayonne prop Christophe Laurent who was a little to physical in his remonstration.
Dourthe gave his team the lead five minutes after the beark with a long-range penalty, and then Fraser, a former New Zealand sevens star, used his nimble feet to skip past a ring-rusty Brian Liebenberg - who had not played since September because of injury - for a try on 50 minutes. Dourthe made it 23-13, and then 26-13 on 57 minutes with another penalty.
Just inside the final quarter, Skrela took the ball at pace off a maul and crashed over the line for his second try, and he added the conversion to make it 26-20 - Skrela had scored all 20 of the Parisians' points!
Bayonne's forwards squeezed out another penalty with thirteen minutes to go, and Dourthe took his team two scores ahead again at 29-20, and the Avirons fought a noble rearguard action, helped by a screaming mass of Basque humanity from the stands.
Bergamasco atoned for his previous error by finishing off a move begun by Ignacio Corleto, and Skrela converted to make sure of the defensive bonus point, but it was too late for dramatic comebacks.
The scorers:
For Bayonne:
Tries: Gerber, Fraser
Cons: Dourthe 2
For Stade Français:
Tries: Skrela 2, Mirco Bergamasco
Cons: Skrela 3
Pens: Skrela 2