Reynaldo Gonzalez is accusing Google, Facebook and Twitter of providing "material support" to extremists.
He alleges they "knowingly permitted" the so-called Islamic State group - referred to as "ISIS" in his legal action - to recruit, raise money and spread "extremist propaganda".
The companies said they had policies against extremist material.
Mr Gonzalez's daughter Nohemi was among the 130 people killed when extremists attacked Paris' Bataclan concert hall, bars, restaurants and the national football stadium in nearby Saint-Denis.