"In all sport, there is no foregone conclusion at any stage unfortunately, and she did run an absolutely superb race, so we can't be too deflated".
"Frankie committed and went for it and with the ground testing her, it's hard to show that turn of foot and Waldgeist has outstayed her on the ground". But, a year after Alpha Centauri won four Group Ones on the bounce, she seems to have cornered the market in two-year-old fillies after Albigna won the Prix Marcel-Boussac.
"I would say she is probably top of the pecking order (of the stable's fillies) as she stayed the mile so she looks more like a Classic filly".
If the five-year-old is given the go-ahead to run again, options would include the Champion Stakes at Ascot on 19 October or the later Breeders' Cup meeting in the United States. "He's a fine horse, trained by Andre and owned by a good friend of mine".
"We've always said that Prince Khalid will make the decision, but whatever happened, it wasn't going to be in a hurry and I think we'll get her back and Prince Khalid will want to reflect on all the various possibilities".
The five-year-old victor delivered French trainer Fabre his first success in the five-million-euro ($5.49 million) showpiece since Rail Link in 2006. "The ground had a lot to do with it".
"I'm very proud that Waldgeist managed to beat such a fantastic mare and it's well deserved in some ways, so I'm delighted", Fabre, who claimed his first Arc in 1987 with Trempolino, told ITV.
"We have to accept defeat in racing".
Richard Hannon's filly had scored at 66-1 over course and distance a year ago, at the chief expense of Laurens in the Qipco 1000 Guineas.
Sean Leavey had Billesdon Brook ideally-placed in midfield, before overhauling another old foe Veracious to win by a length and a half - with Iridessa a further half-length back in third.
"The expectation is so enormous with these things, there is a wave of goodwill, and the good wishes that we all had was just unbelievable really and therefore it was not quite what we hoped, we've got to be honest about".
Elsewhere, Saturday was a day of milestones - not least for Dettori.
Waldgeist, who has won a number of big races in France including this year's Prix Ganay, is co-owned by German Dietrich von Boetticher.
There was also a Group Two win for Martyn Meade's Technician in the Prix Chaudenay, but Mark Johnston's Dee Ex Bee was unable to take advantage of the absence of the brilliant Stradivarius in the Prix du Cadran.