Fly-half Gavin Henson scored the first points for the Exiles at this level, but Lyn Jones' men trailed 35-16 at half-time.
Stade Francais hooker Remi Bonfils and centre Waisea Vuidarvuwalu both crossed twice to secure the bonus point before Hugo Bonneval touched down for a fifth first-half try.
Daniel George scored Welsh's first try, but Felipe Contepomi added the gloss on an excellent individual display with a 75th-minute score in a 25-point haul as Stade started their Pool Five campaign in style.
London Wasps claimed maximum points with a commanding 38-25 home win over Newport Gwent Dragons in Pool Three.
Dai Young's men were too hot handle for the Welsh region at Adams Park and deserved their four-try victory.
Jack Wallace, Fabio Staibano, Billy Vunipola and Joe Simpson all crossed for the 2003 champions.
The Dragons got off to a flyer when qualified pilot Andrew Hughes scorched over for a second-minute try but that was as good as it got for Darren Edwards' outfit.
Nicky Robinson kept Wasps ahead with his reliable boot and, once Simpson touched down for the bonus points, the home side were 20 points clear.
The Dragons scored a consolation through teenager Jack Dixon but Wasps join Bayonne at the top of the pool.
London Irish made light work of Bordeaux in Pool One with a 43-9 away win.
Sailosi Tagicakibau scored twice while Chris Hala'ufia, Topsy Ojo, Halani Aulika and Jonathan Joseph all crossed for the Exiles at the Stade Andre Moga.
Irish, who lie in a lowly 11th spot in the Aviva Premiership table, fell behind to two early Lachie Munro penalties before bursting into life.
Number eight Hala'ufia was the first to touch down in the 14th minute before wing Ojo put the visitors ahead seven minutes later.
The English outfit did not look back in the second half as Ian Humphreys, who converted the first two tries, added a penalty two minutes after the restart to steer the away side into a commanding 17-6 lead before they surged clear late on.
Bath claimed their first away win in Europe in almost two years with a convincing Amlin Challenge Cup 40-17 bonus-point success over Bucharest Wolves.
Sam Vesty scored 20 points as the Aviva Premiership outfit strolled to a five-try victory at Arcul de Triumf.
The 2008 winners had not won on the continent in European competition for five matches since their triumph against Aironi in the Heineken Cup.
Lock Will Spencer and hooker Ross Batty scored first-half tries before Vesty, Ollie Devoto and Kane Palma-Newport all crossed to seal maximum points for Gary Gold's troops.
Bucharest scored twice themselves through Florin Surugiu and Christian Munteanu, but Bath have applied pressure on their group rivals Calvisano and Agen, who face each other in the late kick-off on Saturday.
Worcester Warriors taught Gernika a severe lesson with a thumping 85-5 success in Amlin Challenge Cup Pool Two.
This was the Spanish champions' European debut, but it turned into a nightmare as the Warriors crossed 13 times.
Gernika wing Toto Mazzochi scored on the hour mark, but the joy was short-lived as Richard Hill's side ran riot in this one-way contest.
Replacement Max Stelling grabbed a six-minute hat-trick late on, wing Andy Short and scrum-half Paul Hodgson scored try doubles while number 10 Joe Carlisle bagged 25 points with a try and 10 conversions.
Yet the challenge in weeks ahead will be tougher for Worcester, who take on Perpignan next weekend.
The French giants thrashed Rovigo in a 10 try 79-12 romp at the Stadio Mario Battaglini this afternoon.
- London Wasps
- Newport Gwent Dragons