Clermont's Harry Plummer kicked a late drop goal to deny Bordeaux-Begles a place in the French Top 14 play-offs, but Clermont also missed out on qualifying.
Plummer, 27, slotted the three points in the 77th minute, two weeks after the hosts won a second consecutive Champions Cup by hammering Leinster.
Clermont won 34-31, but despite the victory, they missed out on the play-offs after Racing 92 beat first-place Toulouse 31-20 to finish in fifth and La Rochelle edged Stade Francais 27-22 to end the season in sixth.
Pau will host Racing on Saturday June 13, while Stade Francais meet La Rochelle again 24 hours later in Paris.
Montpellier joined Toulouse in the automatic semi-final spots, after winning 28-25 at Lyon.
Bordeaux-Begles head coach Yannick Bru said his team had been "stupid" at the start of the season, when they lost five of their opening 11 games.
By the interval, Bordeaux-Begles looked on course for a top six spot, leading 24-14 thanks to tries from scrum-half Maxime Lucu, No 8 Temo Matiu and flanker Pierre Bochaton.
Clermont cut the advantage to six points with half an hour to play, but Plummer's late drop goal stunned the 32,000-capacity crowd and denied his side a place in the knock-outs.
