Francotirador is a loanword from the French, franc-tireur, meaning "free shooter". During the Napoleonic wars, francs-tireurs referred to light infantry, or skirmishers who would have fought out of formation (citation).
The word acquired its meaning of a partisan, or an irregular soldier who is fighting out of uniform (and therefore exempt from rules regarding treatment of prisoners), during the Franco-Prussian War (1870). During that conflict, members of French shooting clubs, who referred to themselves as francs-tireurs, engaged in guerrilla warfare against Prussian troops -- and were summarily executed if captured. During the Second World War, many French Resistance fighters referred to themselves as franc-tireurs.
It appears that the Spanish francotirador has the original meaning of sniper or sharpshooter, probably acquired during the Peninsular War (1807 - 1814), but not the latter meaning of a partisan or guerrilla. (In fact, so long as I'm mentioning the Peninsular War, I'm going to point out that the word guerrilla was popularized in both Spanish and English due to that conflict).
So although there is a connection between the word francotirador and France, it's a historical link -- the word doesn't literally mean "French shooter". At least not originally; I wonder how many native speakers would be aware of that.