By some margin, the oldest non-French 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 pages.