The literal translation from the French is "look for the woman". It is used when a man behaves unusually or gets into a quarrel or other difficulty and the reason for it is sought.
'Look for the woman' express the idea that behind a problem in question there is a woman. That isn't to say that the woman herself was necessarily the direct cause of the problem, as in Shakespeare's Macbeth for instance, but that a man has behaved stupidly or out of character in order to impress a woman or gain her favour.
The expression was coined by Alexandre Dumas (père) in Le Monte-Cristo, 1857:
"Vous connaissez sa maxime, lorsqu'il veut découvrir un secret quelconque: cherchez la femme; dans ce cas la femme n'a pas été difficile à trouver."
(You know his maxim, when he wants to discover an unspecified secrecy: seek the woman; in this case the woman was not difficult to find.)
The phrase was adopted into English use and crossed the Atlantic by 1909. It was well enough known there by that date for O. Henry (William Sydney Porter) to use it as the title of a story - Cherchez La Femme, which includes this line:
"Ah! yes, I know most time when those men lose money you say 'Cherchez la femme' - there is somewhere the woman."