Calling it a mont was perhaps a bit of a stretch, but when European settlers first came to Melbourne, this scrubland to the south of Ringwood was indeed a heathland. Calling it Heath-Mont was simply an attempt by the property developers of that era to give it a little class. (Nearby Heatherdale gets its name via a similar path, and not, despite what you may have heard, from lovers named Dale and Heather.)
It is also important to note that despite the competing claims of a number of early local families, the area was not named after anyone named Heath – indeed, parish records of the time clearly establish that the name attracted men named Heath to the area, not the other way around.
But this does not answer the question of why it would be the French mont rather than the English mount. Various theories involving early settlers being of French extraction have been proposed over the years, but again, parish records disprove the theories handily. Most likely, it was inspired by Vermont, which was already a successful area for property developers at that time, and which prospective customers would often pass through on their way to sales at Heathmont. No doubt the developers hoped that a little of that success would rub off onto this new area. Which in retrospect, seems unduly optimistic of them.
Suburbs near Heathmont: