If you look at a score, it says Harpes I and Harpes II, not specifying how many, but definitely more than one. But if the tempo is too fastastique, it won’t necessarily help! He wrote about it in his memoirs, which are fun to read and illuminating. I’ll see if I can correct the article partway.
Remember that the harps we are talking about would have been Grecians (Erard’s initial double-action model) which were smaller and less powerful. The “big-gig” harp that you tend to see in most photos of concert artistes of the time was the larger and louder Gothic, which didn’t make its appearance until five or six years after Symphonie Fantastique premiered.
Therefore they would certainly have needed a whole battalion of harps.