by RON FLATTER

Imagine this. It’s three days before American Pharoah runs for the first Triple Crown in 37 years. Can you see Bob Baffert showing up to train some other horse at a county fair? 

That is essentially what Criquette Head-Maarek did on Thursday, October 1, at Hippodrome de Compiegne an hour north of Paris three days before she will saddle Trêve in attempt to win the Prix de l’Arc de Triomphe—Europe’s richest horse race—for an unprecedented third year in a row.

The track that shares its name with the village of about 40,000 is a game that plays host to 21 days of small-time races throughout the nine-month flat season in France. Head-Maarek was there on Thursday to saddle a filly who beat one home in a $25,000 handicap. On Sunday, Treve runs in the $6.7-million Arc.

“It’s a nice track,” she said. “For us it’s a province track, but it’s very well laid out.”

With only one reporter following her around on a breezy but comfortably crisp afternoon, it was a quiet break from the bright spotlight and seemingly endless stream of media and fans that have wanted a piece of her for months.

“Lots of people are coming to look at her,” Head-Maarek said of the five-year-old mare. “She brought a lot of people from all over the world.”

The attention will only intensify for this 67-year-old survivor of a brain tumor and cancer whose three wins in the Arc (she also won with Three Troikas in 1979) are exactly three more than any other woman has ever trained. She fits right in to French racing’s first family; the Heads have won 10 of the first 93 runnings of the Arc.

The work to keep Trêve at the top of her game this year has not been as complicated as last year. That is when foot trouble limited her, and despite going the final five furlongs in an eye-popping 56.79 seconds in the 2014 Prix Vermeille, Trêve finished fourth in that final prep for the Arc, which she won at 16-to-1 odds in Europe (her price was shorter in America because of coupled entries).

Now, after jockey Thierry Jarnet went into cruise control last month for an easy win in that same prep, Head-Maarek figures Trêve is as good as she was as a three-year-old, when she overcame a rough, early trip from a bad draw to win the first of her two Arcs to date.

“She’s grown now that she’s 5,” Head-Maarek said. “She’s put weight on, and she’s more mature now than she was before. Her foot is OK. We’ve found the right shoes to put on her. Everything is so far going perfectly well this year. She’s won the three races she’s won. She’s coming to a peak for the Arc.”

Bettors here in Europe believe it. They have made Trêve about an even-money favorite to make history Sunday against the likes of challengers Golden Horn, the winner of the controversial Irish Champion Stakes, and New Bay, victorious in his last three races.

 “Mind you, we don’t know the colts,” Head-Maarek said. “That’s my concern.”

But even as she tamps down public enthusiasm with her family’s typically nice modesty, Head-Maarek always seems to be comfortable in the pressure cooker, wearing the expectations well.

Then again, she has Trêve. As she puts it, “A good horse makes good trainers.”