Clemenceau used the UK short-run BS-5 catapult… the same as the bow catapult on Eagle and Ark Royal in their final versions, so they were fully capable of operating Buccaneers, however the catapults and arresting gear were capable of handling the Phantoms only with a very light payload.

The Phantoms only launched with a full payload from the angle catapult on Eagle and Ark Royal (long-run BS-5 catapult).

Type Run Length Capacity
BS4 103ft 160ft 40,000lb@78kt Hermes [starboard]
BS4 145ft 200ft 50,000lb@97kt Hermes [port only] 1966
BS5 199ft 268ft 50,000lb@105kt Eagle 1964 & Ark Royal 1970 [angle only]
BS5 151ft 220ft 50,000lb@91kt (33,000lb@150kt) Eagle 1964 & Ark Royal 1970 [bow only]; Foch & Clemenceau

Foch & Clemenceau were both larger than Hermes, which did operate Buccaneers after her port BS-4 catapult was lengthened in 1964-66.

Hermes could launch Buccaneers from both her catapults before and after her 64-66 refit, the longer portside cat gave a better safety margin in low wind conditions. Also, Shock Horror! Hermes refit was intended to allow Phantoms to operated off her deck (she only needed the JBDs upgrading and bridle catchers to be fitted, originally scheduled for her 68 refit), and before anyone states she was too small to operate F-4s, she already had operated them in 1963 BEFORE her catapults were upgraded. F-4Bs, as well as other USN types cross decked to Hermes from the USS Ranger, and returned without difficulty.
After the ‘Healy Axe’ of 1966 a lot of untruths were pedalled to justify the premature phasing out of the British carrier fleet, and as Hermes was only a few years old retiring her after only ten years in service would have been difficult, so officially she became ‘too small’ to operate Phantoms (despite having done so already) and was effectively ‘disarmed’ to become a troop transport in 1971-73 (commando carrier) to replace her half sister HMS Albion (herself barely 19 years old at the time, good for another ten years at least). None of the RNs carriers were in desperate need of replacement at the time, Victorious had completed an eight year refit in 1958 (effectively a SLEP) that at the time was said to have extended her life by twenty years (to 1978), Eagle had been similarly refitted 1959-64 (so would be usable until 1984) and Ark Royal had a truncated refit 1967-70 which still kept her going until 1978.
If Hermes had recieved Phantoms, they may have been limited to the Air defence role only, but she had a Buccaneer sqn for strike missions anyway, so this would be acceptable. The F-4s could have launched with a full bomb load but reduced fuel and top up their tanks from Buccaneer tankers if needed (a technique used aboard Eagle in 64-66 when she operated S1 Buccaneers and Scimitar tankers).