The latest incident involved a mare that had already died of natural causes in Roanne, near Lyon, last Friday.
The body had been left in a field awaiting professional removal, but its owner noticed on Monday that the ear, eye and nose had been removed.
Local police said they are linking the case to “about 15 other mysterious acts of torture and mutilations of live horses around France these last weeks”, according to AFP.
Another incident last week, this time in the Jura region, involved a horse being stunned before an eye was gouged out and a piece of bone removed. The animal later died.
No meat was taken from the carcases.
Local police posted a “call for vigilance” on social media and said breeders and equestrian centres have been alerted.
Gendarmerie du Jura posted on Facebook on Monday: “We invite you to report any individual or behaviour deemed suspicious near pastures hosting equine, stud, farm or equestrian centres.”
Other acts have included donkeys and one incident in Cortambert, Burgundy earlier in the month involved a horse having its right ear cut off, one of its eyes gouged out and its genitals removed.
“This is absolutely barbaric,” a local official said at the time.
A Paris police spokesperson said there were cases of similar killings and mutilations between 2014 and 2016 and past incidents in Belgium and Germany.
But the high number in France since the beginning of the year is unprecedented over such a short period.
The police spokesperson added: “We do not understand the motivation.
“Is it a satanic rite, insurance fraud, some macabre trophy hunt or an internet challenge?
“We don’t know. It is very traumatising.”
Additional reporting by agencies