I like this word. It is easy to imagine how it came about, easy to visualise people shouting it out, the rush and confusion, the warnings that led to its eventual meaning.
So where does it come from? Well, it is not a difficult word to trace. It comes into English, through Middle English, from Old French alarme, which in turn came from Italian. You might think that it doesn’t look very Italian in its current form, but it was originally all’arme, which meant “to arms!” It would have been shouted out in warning, or to rouse the soldiers to prepare. Gradually, of course, it lost its sense of weaponry and kept the idea of warning and rousing, which of course extended to waking.
Taking it one step further, all’arme came from the Latin preposition ad, “to”, plus the definite article; arme from Latin arma, which meant “weapon”. From weapon to warning seems to me a logical step.
Glossologics 
When I was looking up the etymology of the word “alarm” I kept coming across a word I’d never heard before. The word being “tocsin” which to me initially looked like the English word ‘toxin’ adapted to fit Welsh orthography? Which of course it isn’t rather the definition of “tocsin” is:
a bell used to sound an alarm; the sound of an alarm (usually a bell); a warning signal.
The etymology is:
Tocsin “alarm bell” 1580s, from Middle French toquassen “an alarm bell, the ringing of an alarm bell” (late 14c.), from Old Provençal tocasenh, from tocar “to strike” (from Vulgar Latin *toccare “strike a bell”) + senh “bell, bell note,” from Late Latin signum “bell, ringing of a bell,” in Latin “mark, signal.” The current English spelling is from 1794, adopted from modern French.
In other languages ‘tocsin’ is:
Greek: κώδων κινδύνου, συναγερμός
Welsh: cloch-rybudd (warning-bell), larwm
French: signal d’alarme, alarme
Italian: campana d’allarme; a martello; (fig) segnale d’allarme
Spanish: alarma
Portuguese: campainha ou sino de alerta, sinal de alerta; sinal de emergência, sino ou campainha de emergência, toque de emergência
German: Sturmglocke
Russian: набатный колокол, набат