You're right that DNA provides a solid source for clues, but its ultimate value depends on documentary confirmation and, to some extent, on how far you're willing to stretch to construct a family tree.
There were eight Menard boys born in St-Philippe between 1814 and 1823. There were no Meunier, Migner, or Monier births at all. The most likely candidate would seem to be François Menard, born on 8 November 1818, son of Pierre Menard and Françoise Guerin.
If this is close enough for you, then proceed!