As mentioned in the Wikipedia articles cited by Peter Lyderik, the 1er RPIMa, located in Bayonne (SW France, not far from the Spanish border) is a special forces regiment belonging to the CFST (Commandement des Forces Spéciales Terre, Army Special Forces Command) which is the Army branch of the COS (Commandement des Opérations Spéciales, Special Operations Command). The COS has also an Air Force branch and a Navy branch, which Commando Hubert – the unit of Petty Officers (Maîtres in French) Cédric de Pierrepont and Alain Bertoncello, KIA last week in Burkina Faso and honoured this morning in a ceremony held at Les Invalides in Paris – belongs to.
The lineage of the French airborne units is pretty complex but, to cut a long story short, the 1er RPIMa (which took part also in the hostage liberation operation last week, along with Cdo Hubert) is considered the heir of the French SAS units created during WW2 and trained at Ringway by the British. They were then named 2e and 3e RCP and participated in a number of operations in WW2, the two most famous being the drop on Brittany, behind the German lines one day before D-Day and operation Amherst in The Netherlands towards the end of the war. La prière du para (the paratrooper's prayer) was created by Aspirant André Zirnheld who belonged to a French SAS unit under the command of Capt Georges Bergé, embedded as the “French squadron” in Major David Stirling's larger SAS unit in North Africa. The text was found in his personal belongings, after he was KIA in the aftermath of an SAS raid against a German military airfield at Sidi-Haneish, Egypt, on July 26, 1942.
The 1er RCP (my former regiment) was created in Morocco in 1943, from pre-existing smaller French airborne units. It was trained and equipped by the Americans, on the same model as the standard WW2 US Army Parachute Infantry Regiment. It's part of the 11th BP (Brigade Parachutiste, Airborne Brigade) and is not a special forces unit per se, but a regular airborne infantry unit (like 3e and 8e RPIMa and 2e REP).
The 6e RPIMa was disbanded in 1999. Petit Caporal, FYI, the regiment wasn't exactly re-activated, it's only that its flag will be kept by the basic training center of 11e BP at Caylus Camp, like the flag of 2e REC, disbanded at the end of the Algeria war because of the downsizing of all French armed forces, is kept by the DLEM (Détachement de la Légion étrangère à Mayotte, Foreign Legion Detachment in Mayotte). 9e RCP does no longer exist. It was disbanded also in 1999, following the switch to an all-volunteer force and the subsequent downsizing.