And now the aristocrats of continental rugby have their hearts set on what would be a remarkable achievement as they attempt to become Kings of Europe and of France at the same time.
"I think at the moment both competitions are a priority for us," Toulouse prop Census Johnston told FRC.
"Doing the double will be difficult for us to pull through but we have the potential in the squad to perform in both competitions, and I think we're in a good position to do both.
"We're top of the table in France and we're in the quarter-final of the Heineken Cup against Biarritz. It will be tough but I'm sure we have the confidence to be able to pull through both."
Johnson admits that the pressure of expectation is always on everyone's shoulders at Toulouse but it's a pressure the players gladly accept.
Toulouse traditionally go into the Heineken Cup as one of the pre-tournament favourites but they face a stiff challenge if they are to retain their crown this time around as they prepare for a quarter-final clash on opposition soil.
Johnson, who recently signed a contract extension with the club, is aware of the size of the task ahead but he confidently predicts that if anyone can defy the odds and double up, that team is Toulouse.
"Toulouse have always been in a situation where they've had to perform at their highest at certain times and I think we're all pretty confident at the moment," added the Samoa prop.
"Obviously the guys know we've got a tough month ahead of us but I think we know what the deal is and it's important that we play well, especially leading up to the Heineken Cup quarter-final.
"Our team has always been able to peak at the right time, so I think we're heading in the right direction at the moment.
"I think you are always expected to win and there's always a lot of pressure week-in and week-out to win. With the quality of players we have at the moment there's always pressure on your position as well.
"You know that as soon as you have a bad game then you could be dropped. You could be starting every game and then have one bad game and lose your position, so I think that's one of the advantages of being in a team like Toulouse.
"There is pressure on us to win every game but we just know how to win, we're a team that knows how to win at the right times."