Investigators said bullet holes in the front of the party office were made by a 9 millimeter automatic weapon in two bursts fired at around 2300 GMT Sunday.
Several other local offices were damaged during labor reform protests over the past weeks.
"Must there be casualties for our concerns to be taken into account and for all to condemn those acts without any ambiguity?" Socialist Party chief Jean-Christophe Cambadelis said in a statement, urging union leaders to condemn such attacks, Reuters reported.
Interior Minister Bernard Cazeneuve said authorities were investigating the attack.