Thoiry zoo said that the case was the first killing of a rhinoceros in captivity by suspected poachers in Europe.
Staff at Thoiry Zoo, 35 miles west of the French capital, turned up at work on Tuesday to find the body of the four-year-old mammal in its enclosure.
A rhino is dead after poachers sawed off one of its horns at a zoo in the suburbs of Paris. His horn - a single kilogram which could be worth as much as $60,000, according to current estimates - had been hacked off with a chainsaw, and a second, partially sawed-off horn had been left behind by the thieves.
Two other white rhinos, 37-year-old Gracie and five-year-old Bruno, were able to avoid the poachers according to the zoo. He came to Paris in 2015 with one of the zoo's other rhinos.
The rhino was shot three times in the head. Scientists say that rhino horn - which is made from the same kind of substance that comprises human fingernails - has no medicinal value.
Rhinoceros horn is highly lucrative and can sell for more than its weight in gold on the black market.
France outlawed the trade in ivory and horns past year.
But demand for the horn is strong in Asian countries such as Vietnam, where it is prized as an ingredient for traditional medicines. They broke through two other locked doors into the building containing the rhinos.
"White rhinos are a spectacular conservation success story, but the current poaching crisis could reverse all of our conservation gains", Matthew Lewis, an African species expert writes on WWF's website.
Vince was born in September 2012 at Burgers' Zoo in the Netherlands, according to The Independent.
Thoiry zoo described the attack as a "heinous act" on its Facebook page.