I am assuming you mean during the interwar period, as the post-war Marine Nationale is relatively well known, operating both second hand British and American carriers before constructing the Clemenceau class in the 1950s. As such I will only address designs between Bearn up until the Fall of France. (There were a couple of hybrid 'battlecarrier' designs during the war, and the post-war designs deserve their own post).

Under the 1922 Washington Naval Treaty France was allowed 60,000 tons of aircraft carriers. Purpose built ships were intended to be constructed to complement Bearn, but a combination of budgetry constraints and the formation of the Air Ministry in 1928 (which took almost complete control of naval aviation) prevented any from being laid down until 1938.

Nonetheless, there was a series of designs, from 'PA1' (Porte-Avions 1) to PA16. There is not a huge amount of information on the designs PA1 to PA15 on these but some, however, are worthy of note.

• PA1 was the first design study, from 1929. This ship was 27,400 tons standard and 244m in length. Of note was the strong gun armament of 8 x 203mm guns and 12 x 100mm guns. This was a rather unique design. The flight was not full length, and there was a catapult located both on the bow and at the stern. The island was located in the port side of the ship.
• PA2 was similar to PA1 in dimensions, but slightly larger, at 28,500 tons. It had no island structure. It was intended to operate 54 aircraft.
• PA3 was a study for a much smaller carrier, of 13,500 tons. It would operate 24 aircraft. It dropped the heavy armament of 203mm guns and the requirement to operate floatplanes.
• PA4 was an enlarged PA3 at 18,000 tons and 38 aircraft.
• PA5 was an enlarged PA4 at 24,500 tons and 48 aircraft. It would have a fighter take off deck from the hangar, in a similar vein to the British Courageous or Japanese Akagi.
• PA5b was probably just PA5 but modified to incorporate a quad 330mm turret (!). This was forbidden under the International Treaty system.
• PA6 was 19,230 tons and incorporated two triple 203mm guns turrets. It would operate 28 aircraft.
• PA7-PA9 have little information available.
• PA10 was a light carrier of 14,000 tons capable of 33 knots. It was likely intended to work closely with the cruisers and destroyers of the Marine Nationale. Aircraft complement was 28. It was flush deck with no island.
• PA11 was an enlarged PA10 of 15,350 tons, capable of 34 knots.
• PA12 was a larger PA10/11 at 17,300 tons. This may have been to enable more armour, but not much is known.
• PA13 was 19,000 tons and designed for 70 aircraft. This was a full size fleet carrier, with a starboard island and full length flight deck.
• PA14 was a variant of PA13 with 76 aircraft.
• PA15 was a 23,000 ton ship, 250m in length, intended to operate 70-80 aircraft. Speed would be 30 knots.

From 1935/36 there were also various schemes to convert two heavy cruisers of the Duquesne class into hybrid carriers. These schemes were named 'A' through 'D'. All retained two of the 203mm turrets except for Scheme C, which had a full flight deck. Aircraft complement would have been 12-14. Such a conversion would have been expensive and time consuming and was set aside. It was briefly revived in Spring 1940 before the Fall of France.

PA16 became the Joffre class. The first ship was laid down on 26 November 1938 at St Nazaire. This design was 18,000 tons standard, 236m long, capable of 33 knots with capacity for 40 aircraft. The class would have been equipped with 8 x 130mm guns, 8 x 37mm guns and 24 x 13mm guns. A second ship, named Painleve, would have followed. In April 1940 a third ship, 'C', was authorised. The Marine Nationale was acquiring new aircraft for these ships, including the American Vought 156F and the Loire-Nieuport 401. Joffre was the only ship of class laid down and was approximately 20% complete when work stopped.

As a cheaper alternative to a full carrier, the French developed the concept of the 'transport d'aviation', a 10,000 ton mobile seaplane base capable of operating large seaplanes armed with torpedoes from the sea and smaller reconnaissance and fighter floatplanes launched by catapult. Only a single ship was completed - the Commandant Teste - which was considered too slow and vulnerable to operate with the fleet. In December 1939 her air group was redeployed a shore and the ship was used as an aircraft transport between France and North Africa.

The information here primarily comes from two sources.

• 'France: The Marine Nationale' by John Jordan, which is Chapter 1 of a book called 'On Seas Contested: The Seven Great Navies of the Second World War'
• 'The French Aircraft Carriers' by Simon Beerbaum

You may also be interested in a couple of articles on the subject.

• 'PA16 Joffre: France's Carrier Project of 1938' by John Jordan, an article in Warship 2010.
• 'From Battleship to Carrier: Bearn', also by John Jordan, an article in Warship 2020.