Castres sporting director Christophe Urios said his side showed a "big pair of balls" by edging to a 19-14 victory over Racing 92 on Saturday to set up a French Top 14 final clash against Montpellier.
Castres struck an early blow through Tongan flanker Maama Vaipulu in Lyon, and despite a fightback from European Champions Cup runners-up Racing, they battled to an attritional victory thanks to 14 points from the boot of Benjamin Urdapilleta.
Castres will take on regular-season table-toppers Montpellier at the Stade de France on June 2 in their first Top 14 final since 2014, having won the title the previous year.
"I'm proud to have achieved this, led so many Castres fans to Lyon and that people see themselves in our team because it releases a form of emotion, and that's what's important," said Urios.
"We have talent, quality, and especially a big pair of balls."
They only snatched the sixth and final playoff place with a late-season charge, before beating Toulouse to reach this semi-final.
The eighth-minute score from Vaipulu was followed by a conversion and penalty from Argentinian Urdapilleta as Castres quickly moved 10-0 in front.
But Racing, who were beaten by Leinster in the European Cup final earlier this month, hit back through winger Juan Imhoff, with Teddy Iribaren slotting over the extra two points.
Louis Dupichot touched down to give Racing the lead for the first time in the match in the 25th minute, but Iribaren's second conversion proved to be their final points.
A brace of penalties from Urdapilleta saw Castres take a 16-14 half-time advantage, before successfully halting Racing in the second period.
A fourth penalty for Urdapilleta with 16 minutes to play ensured that Racing would need a try to draw level, and Castres clung on in the face of a late onslaught to book their ticket for the final.
"The last five minutes? What's driving you is what's inside you: the Stade de France, the trophy," said Castres captain Mathieu Babillot.
"That's what I shouted in my prop's ear: 'two minutes, two minutes! Stade de France! Final!'. And that's it, things went our way and it's just unbelievable."
On Friday, Montpellier thrashed Lyon 40-14 to back up their excellent regular season by qualifying for the final for only the second time.
Vern Cotter's men will be bidding for their maiden French top-flight title, after finishing a point clear of Racing in the league table.