External resources are always a help. Try here: https://www.thoughtco.com/introduction-to-french-verbs-1371059
Indeed, to march in is another option, but it means, if I'm not mistaken, and according to TheFreeDictionary, " To proceed directly and purposefully", a sense which is not conveyed by the French verb (we would say something like marcher d'un pas décidé).
My understanding is that any meaning that diverges from to walk will be unexpected, except in a military or protesting contest. HTH!