European militaries started to professionalize in the 17th and 18th centuries. This included the intellectual study of military science. The foremost writers and thinkers in this study were French. The most famous of these was the Signeur de Vauban. Vauban's writings shaped how fortifications were both built and besieged throughout the Age of Gunpowder. His highly technical writings either invented or popularized a host of military terms.

For more, a good starting point is Russell Weigly's The Age of Battles.

Since my first answer got down voted into oblivion(Y'all need jesus) I'll try again.

English was initially an entirely Germanic language called Old English. In 1066, French Normans invaded and conquered Britain. The French brought with them many new words which would become incorporated into the English language. This new language is called Middle English and is the basis of Modern day English.

Examples: (From oxforddictionaries.com)

Soldier: Middle English: from Old French soldier, from soulde '(soldier's) pay', from Latin solidus

Officer :Middle English: via Anglo-Norman French from medieval Latin officiarius, from Latin officium

Sergeant: Middle English: from Old French sergent, from Latin servient- 'serving', from the verb servire.

General: Middle English: via Old French from Latin generalis, from genus, gener- 'class, race, kind'. The noun primarily denotes a person having overall authority: the sense 'army commander' is an abbreviation of captain general, from French capitaine général 'commander in chief'.

Of course, for newer terms like "Artillery" and "Infantry" you should look at TRB1783's answer.