The bill now passes to Governor Bobby Jindal, a conservative Republican, for his veto or signature into law.
Many people in Louisiana are descended from French people from southwestern France who settled there.
Jindal has thrown out previous versions of the bill, but Democrat Stephen Ortego, who is behind this version, hopes this one will get through as it allows translations in French but no other language.
He has support from around a dozen of his colleagues from Acadiana, a large region of Louisiana where French colonists settled.
Ortego was inspired after a trip to New Brunswick, in eastern Canada, where road signs are bilingual.
In the 18th century, a group of French-speaking colonists moved to Louisiana from New Brunswick after refusing to pledge allegiance to ruler Britain.
According to Ortego, at least 22 parishes in Acadiana are interested in putting up bilingual road signs.
Louisiana's most famous city, New Orleans, isn't planning to change its name but other parishes might choose to direct drivers to “Nouvelle Orleans”.