Not for the first time, they come to Belfast seemingly holding a well-stacked hand yet that has rarely been sufficient.
They simply ooze talent, with Antoine Dupont, World Cup winner Cheslin Kolbe, Romain Ntamack, Maxime Medard, Thomas Ramos, Julien Marchand and so on.
Fine, but when has that mattered on an unforgiving winter's night at Kingspan Stadium?
The chatter emanating from Toulouse is that they badly want another Heineken Cup to add to the four they have already bagged - success being well overdue as the last one was back in 2010 - and that losing out in the last two tournaments at the semi-final stage is something they reckon can be improved on this time around.
Those defeats, to Leinster in 2019 and Exeter Chiefs as the Covid-hit 2020 competition was completed in September, have created a new itch which the rejuvenated powerhouse French club badly want to scratch.
With this season's European group stage streamlined to only four games, there is no real margin for error if Toulouse are to keep on track to achieve their goal a mere three years after they found themselves in the doldrums of the Challenge Cup and underachieving big time while there.
Saracens not being around can surely only be of assistance, but Leinster and holders Exeter - the latter who Toulouse play in rounds two and three - aren't going to make matters any easier for coach Ugo Mola and his impressive squad.
Toulouse simply have to come away from Belfast tonight with the right result in order to go forward to taking on Exeter at home and then, especially so, when they travel to Sandy Park.
That they overwhelmed Ulster at the Stade Ernest-Wallon in September's quarter-final - where Kolbe did so much damage - is, of course, of significance, but coming to Kingspan Stadium is a different beast altogether, though a ground without a heaving and highly partisan crowd makes things more palatable for the visitors.
Flanker Rynhardt Elstadt said of playing in front of a packed crowd: "I think if you have home advantage it gives you that X-factor and a bit more energy.
"You lack that bit of energy you used to get from the crowd. I think it plays a very big role," he added, which suggests that 500 in Kingspan Stadium isn't going to be of huge help to Ulster.
Indeed, the home team will have to have their best inner beast on display and halt Toulouse from functioning because, well, they can play a bit.
They have lost only three from 11 rounds of the Top 14 and have shown they can win on the road.
A quality pack, with Marchand and Cyril Baille and, naturally, grunt on the bench too, can discomfort Ulster and then, behind the scrum, there is so much with Dupont and Kolbe almost unplayable.
Ntmack in the centre and Ramos at 10 - as was the case last weekend in the win at Bayonne - is an interesting call but, then, they will want to play, not just suffocate, though defensively it might not work so well.
That could, of course, be their Achilles' heel, but this Toulouse just look that bit more equipped to avoid the usual pitfalls.