march (v.) Look up march at Dictionary.com
"to walk with regular tread," early 15c., from Middle French marcher "to march, walk," from Old French marchier "to stride, march," originally "to trample, tread underfoot," perhaps from Frankish *markon or some other Germanic source related to obsolete Middle English march (n.) "borderland" (see march (n.2)). Or possibly from Gallo-Roman *marcare, from Latin marcus "hammer," via notion of "tramping the feet." Meaning "to cause to march" is from 1590s. Related: Marched; marching. Marching band is attested from 1852. Italian marciare, Spanish marchar are said to be from French.
march (n.2) Look up march at Dictionary.com
"boundary," late 13c. (in reference to the borderlands beside Wales, rendering Old English Mercia), from Old French marche "boundary, frontier," from Frankish *marka or some other Germanic source (compare Old High German marchon "to mark out, delimit," German Mark "boundary;" see mark (n.1)). Now obsolete. There was a verb in Middle English (c. 1300), "to have a common boundary," from Old French marchier "border upon, lie alongside." This is the old Germanic word for "border, boundary," but as it came to mean "borderland" in many languages new words were borrowed in the original sense (compare border(n.), bound (n.)"border, boundary"). Modern German Grenze is from Middle High German grenize (13c., replacing Old High German marcha), a loan-word from Slavic (compare Polish and Russian granica). Dutch grens, Danish groense, Swedish gräns are from German.
march (n.1) Look up march at Dictionary.com
"act of marching," 1580s, from march (v.) or else from Middle French marche (n.), from marcher (v.). The musical sense first attested 1570s, from notion of "rhythmic drumbeat" for marching. Transferred sense of "forward motion" is from 1620s.
March Look up March at Dictionary.com
third month, c. 1200, from Anglo-French marche, Old French marz, from Latin Martius (mensis) "(month) of Mars," from Mars (genitive Martis). For March hare, proverbial type of madness, see mad (adj.). The the proverb about coming in like a lion, going out like a lamb is since 1630s.

Replaced Old English hreðmonaþ, the first part of which is of uncertain meaning, perhaps from hræd "quick, nimble, ready, active, alert, prompt." Another name for it was Lide, Lyde (c.1300), from Old English hlyda, perhaps literally "noisy" and related to hlud "loud" (see loud). It fell from general use 14c. but survived into 19c. in dialect.