According to Google Translate , Rouge mont literally translates to ‘Red Mountain’. However, I think mont often means hill or mount, rather than mountain, as in Mont St Michel or Montmartre, neither of which would qualify as mountains.
Rougemont Close seems to be named after the Rougemont House which was once the headquarters of the sadly missed Ottakers bookshop chain, but is now the premises of the solicitors Bonallack and Bishop.
I don’t know why Rougemont House was so-called. It is at the top of Milford/Kelsey hill, but whether it is particularly red, I don’t know.