Marcher means to march but it is used less in French in this sense than it is in English.
In French however, you use marcher for "march" in general, but you faire une marche de protestation, or s'approcher in lieu of marching up to someone or something.
But these measures proved inadequate, and in 1533 the lord marcher, Ostafi Daszkiewicz, the hero of Kaniev, which he had successfully defended against a countless host of Turks and Tatars, was consulted by the diet as to the best way of defending the Ukraine permanently against such inroads.
It was in the successful effort to open this treasure-house that Hamilton's mind received its final temper, " Des-lors it commenga a marcher seul," to use the words of the biographer of another great mathematician.
In 1163 he had completed the conquest of South Wales; the marcher lords were now in possession of the greater part of the land; the surviving Welsh princes did homage for the rest.