"Brave" has a very long story.
The original root is from Greek "βάρβαρος" (barbaros). Βάρβαροι were the people whose language was unintelligible (Βάρβαροs is a well known example of Greek word of onomatopoeic origin) since all you could apparently grab was "bar-bar".
Although it obviously had a pejorative connotation, the main meaning however was simply "foreigner" (as in "non-Greek" of course).
Imported in Latin, the noun barbarus retained this meaning of "foreigner" (although remarkably for the Romans the Greeks were the only "non barbaric" foreigners ;-). In Late Latin however, the adjective, now contracted to "brabus", had the meanings of "savage", "courageous", "indomitable".
Studies about phonetic evolution from Late Latin to Medieval Italian have well documented1 how the plosive 'b' in intervocalic position nearly always evolved into a labiodental fricative 'v', caballum => cavallo (horse) and how the final "us" evolved into "o" (marius => mario, marcus => marco...).
Following these rules "brabus" evolved into "bravo".
In 14th century Italian, it then came to mean "flamboyant", "well dressed" or even "arrogant" as an adjective as well as "mercenary"2 as a noun.
However in modern Italian the meaning is "good at things" (Questo ragazzo è molto bravo in informatica).
During the Renaissance, French kings were obsessed with the conquest of Italy and their armies met the Italian armies on many occasions. When Italian soldiers were showing off in front of the enemy they companions would cheer "Bravo !!!" and congratulate each other.
So that the French interpreted the "Bravo" interjection in many ways: "noble", "courageous", "handsome", "arrogant". Eventually, only the main meaning of "fearless on the battlefield" remained3. Hence the French "bravoure".
One way soldiers would demonstrate "bravoure" in front of their fellow countrymen would be to expose their bare chest to the enemy line, daring them to fire.
Which in my view explains the metaphor "brave my fire" as Peter Taylor has rightly pointed out in his answer.
1: József Herman, Le Latin Vulgaire, 1967 - English Translation Roger Wright, Vulgar Latin, 1997.
2: Dictionnaire Historique de la Langue Française (Robert, 1993).
3: Of course we also interject "Bravo !" to express our admiration, even to female artists to the great surprise of Italians who would rather expect "Brava !".