Bristol crashed out of the European Challenge Cup after slipping to a 29-18 defeat to Narbonne at the Memorial Stadium.
The west country side had to win to reach the quarter-finals as one of the best runners-up but a weakened team eventually lost out despite twice leading at home.
They are the only English side not to make a final eight that includes two French clubs, Bayonne and Brive, as well as Irish province Connacht.
Wing Sean Marsden gave Bristol the perfect start with an interception try in the eighth minute before Tommy Hayes extended that lead with a conversion and two penalties.
But Christophe Ruiz hit back for Narbonne with a converted try before combining with Frederic Lartigue to send Julien Pathe over five minutes later.
Marsden again gave Bristol hope when he finished off a blistering attack on 58 minutes. Ollie Hodge charged forward before Hayes and Mark Denney opened space out wide for the wing.
But English lock Andrew Springgay capped an immediate response from the Narbonne forwards when he was shoved over from a driving lineout on 64 minutes.
Julien Candelon then made sure with a try in the final minute, to bag a bonus point for the French side, as Manuel Contepomi was still walking to the sin bin following his yellow card.