French anti-terrorism judges placed two Frenchmen released by the US military from Guantanamo Bay under formal investigation on Saturday, one step short of laying formal charges under French law.
Another judge was due to decide later on Saturday whether to release Nizar Sassi and Brahim Yadel on bail or keep them in custody.
The investigation was ordered on grounds of suspected "association with criminals engaged in a terrorist enterprise".
Sassi and Yadel were among four Frenchmen sent back to France on Tuesday after more than two years at the US military jail at Guantanamo in Cuba.
The other two former Guantanamo detainees, Mourad Benchellali and Imad Kanouni, were also due to appear before anti-terrorism judges Jean-Louis Bruguiere and Jean-Francois Ricard.
Lawyer Jacques Debray, acting for Benchellali and Sassi, saw the men for the first time on Friday and said they described their time at Guantanamo as hell.
The four were captured during the US led-war in Afghanistan in late 2001 and held by American forces on suspicion of fighting for the ousted Taleban government.
French President Jacques Chirac said this week the four had been returned to France after lengthy talks with US authorities and pledged they would face French justice. Three other Frenchmen remain in Guantanamo.