By some margin, the oldest usage found so far is in the county of Essex, England, where we find Montpelier’s Farm. This has its origins in the 12th century, and is named after a settler of the Norman period.
For the first example of somewhere being named after the French place, rather than a French person, we have to fast-forward a few centuries to 1684, when the earliest of several Jamaican estates of this name is recorded.
Nearly 20 years later, in 1702, comes the first mention of Montpellier's coffee-house, in the city of London, not far from the Royal Exchange.
Not long after, but a continent away, we find Montpellier farm, Cape Province, South Africa established by a Huguenot migrant in 1714, followed by Montpelier Hill, Co. Dublin, Eire, and a Georgian terrace, Montpelier Row, Twickenham near London, both of 1720.
Earliest US example appears to be a mid-1700s house in Howard County, Maryland.
For more on all of these, check out the Gazetteer (see links at right).