And they have installed Leinster as massive short odds favourites for the Irish club to claim a fourth European crown.
"We are very happy to reach a final but I am honestly not very confident because it is Leinster," said coach Christophe Laussucq.
"It is wonderful to reach the final but I truly hoped Biarritz would win the semi-final because Leinster are such a good team that I think we now have just a 10% chance of winning the final in Dublin.
"We know the quality of their team with internationals and British Lions throughout the team.
"They also have the experience of playing - and winning - on the biggest occasions like Heineken Cup finals."
Sergio Parisse and his team-mates suffered heartbreak in the 2011 tournament final in Cardiff when Harlequins edged them out 19-18. That followed the agony of two Heineken Cup final defeats, 34-30 to Leicester Tigers in 2001 and 18-12 after extra time to Toulouse in 2005.
"It is going to be a special moment for us to play in another European final," added Laussucq.
"It has been a very difficult season for us, we have been criticised a lot in France but after all that, we could be the first Stade team to win a European title. This young team has the chance to make history."