Английский Этимологический словарь - march (v.)

- c.1410, from M.Fr. marcher "to march, walk," from O.Fr. marchier "to trample, stride, march," perhaps from Frank. (cf. O.H.G. marchon "to mark out, delimit"), and, if so, related to obsolete M.E. march (n.) "borderland" (see mark (1)). Or possibly from L. marcus "hammer," via notion of "tramping the feet." The musical meaning began 1572 in sense of "rhythmic drumbeat" for marching.