The photos below will demonstrate that it appears to be at about the same level as some other nondescript stumps in the walls - this one being the only one with a personality.
He is definitely not a gargoyle, not in the traditional sense of those fearsome waterspouts, as his mouth has no real opening. The head might be that of a decapitated saint. That would explain his pained look.
Could he have been one of the abbots from centuries ago? Or one of the original builders or architects? As is so often the case, the answer may remain a mystery, which is one of the most endearing aspects of French history.
The abbey dates back to the 11th century, but I do not know how old the wall is that holds the head, nor if the head is older than that wall. These are the kinds of questions one never needs to ask oneself in Los Angeles.
Come to think of it, if I saw this on a wall in Los Angeles, I'd think it was somebody's idea of a super Chia pet. You don't expect that kind of nonsense in France. Next time we're there, I'll ask the mayor.