Hariri was invited by President Emmanuel Macron who was to meet him shortly after midday and then lunch with him and and his wife Lara.
A source close to the premier told the AFP news agency that his two youngest children, Loulwa and Abdelaziz, born in 2001 and 2005 respectively, had stayed in Riyadh "for their school exams".
His elder son Houssam, born in 1999, was due to arrive in Paris from London on Saturday.
Hariri's resignation, announced in Riyadh, sparked accusations that he was being held there against his will.
"To say that I am held up in Saudi Arabia and not allowed to leave the country is a lie," Hariri tweeted just before his departure, adding to repeated denials of the rumours from Saudi officials.
He reportedly met Saudi Crown Prince Mohammed Bin Salman before he left.
Saudis recall Berlin ambassador
Riyadh on Saturday recalled its ambassador to Berlin in protest at comments by Germany's Foreign Minister Sigmar Gabriel which were interpreted as a suggestion that Hariri acted under Saudi orders.
Without mentioning Saudi Arabia directly, Gabriel on Thursday said he shared concerns about the threat of instability and bloodshed in Lebanon and warned against "adventurism".
"Lebanon has earned the right to decide on its fate by itself and not become a pinball of Syria or Saudi Arabia or other national interests," he had said earlier.