Owned by Godolphin, the Siyouni colt burst on to the scene when winning at Chantilly by eight lengths last month.
The Group Three Craven over a mile has long been considered a key trial for the Classics and last year it saw subsequent Derby winner Masar beat multiple Group One winner Roaring Lion into third.
Voicing his concerns about possible underfoot conditions for Epic Hero, Fabre said: “I was really wanting to run him in the Craven but I’m a little bit worried about the ground at Newmarket – it’s a bit quick at the minute.
“So, I’ll make a late decision. The other option is to run at Longchamp on Sunday.
“I doubt he will stay any further than a mile this season – he has lots of pace.”
One Fabre already has booked in for the Prix de Fontainebleau this weekend is Persian King, who beat Magna Grecia in the Autumn Stakes in October.
Whether he returns to Newmarket for the Guineas, though, is still in some doubt.
“Persian King will run on Sunday – he’s an easy horse to get fit,” said Fabre.
“Looking at the ratings of the other (Guineas) horses, he’s a good bit behind a couple of good Irish and English horses – so I’m not thinking of Newmarket at this stage.
“We’ll see what happens. This is his prep race, and I’ll keep an eye on Newmarket.”