In 1870-1, the most comprehensive outline for Modern Rules of War was that formulated by Francis Lieber in 1863 (the Lieber Code, Section IV), and commissioned by President Lincoln, unilaterally directed for the conduct of Union Armies. Our modern, stricter, guidelines for conduct of war between civilized nations only begins a generation after 1870-1, with the series of International Hague and Geneva Conventions that began in 1899.
Lieber attempts to clearly formulate the distinction between partisans - public enemies entitled to the full protection as prisoners of war when captured - and any other miscellaneous brigands and prowlers who were NOT public enemies and thus NOT entitled to such protections.
Partisans are soldiers armed and wearing the uniform of their army, but belonging to a corps which acts detached from the main body for the purpose of making inroads into the territory occupied by the enemy. If captured, they are entitled to all the privileges of the prisoner of war.
Men, or squads of men, who commit hostilities, whether by fighting, or inroads for destruction or plunder, or by raids of any kind, without commission, without being part and portion of the organized hostile army, and without sharing continuously in the war, but who do so with intermitting returns to their homes and avocations, or with the occasional assumption of the semblance of peaceful pursuits, divesting themselves of the character or appearance of soldiers - such men, or squads of men, are not public enemies, and, therefore, if captured, are not entitled to the privileges of prisoners of war, but shall be treated summarily as highway robbers or pirates
Armed prowlers, by whatever names they may be called, or persons of the enemy's territory, who steal within the lines of the hostile army for the purpose of robbing, killing, or of destroying bridges, roads or canals, or of robbing or destroying the mail, or of cutting the telegraph wires, are not entitled to the privileges of the prisoner of war.
War-rebels are persons within an occupied territory who rise in arms against the occupying or conquering army, or against the authorities established by the same. If captured, they may suffer death, whether they rise singly, in small or large bands, and whether called upon to do so by their own, but expelled, government or not. They are not prisoners of war; nor are they if discovered and secured before their conspiracy has matured to an actual rising or armed violence.
In order to earn the privilege of being a public enemy, and be entitled to treatment as a prisoner of war when captured, certain obligations had to be met. Along with wearing a uniform that, in some clear manner, distinguished one as a soldier it was also necessary to be "sharing continuously in the war". This is a key concept that civilians forget - as soon as one "goes home, removes one's uniform, and hides the gun in the closet" one is dis-entitled from being recognized as a partisan entitled to protection as a public enemy; even after getting up the next day and resuming the pretence of being a soldier.
One of the particular details which Lieber clearly gets right was in dealing with the lack of supplies for Confederate armies. In order to remain clothed while serving, many Confederate soldiers found it necessary to loot dead Union soldiers for their uniforms, putting them in the position of marching into combat in the uniform of their enemies. Lieber found no fault with this, provided simply that a clear, distinctive strike of some sort be worn or attached over such, to clearly mark the wearer as a hostile combatant.
Troops who fight in the uniform of their enemies, without any plain, striking, and uniform mark of distinction of their own, can expect no quarter.
So no; by the best rules of engagement available at the time, the Prussians were quite entitled to treat the franc-tireurs as brigands. Their very resistance to authority and commissioning as formal troops that drove the French military command to distraction also disqualified them from consideration as partisans under the Lieber Code.