My English edition of Flottes de Combat 1980/81 offers the following line up/info:
Submarines might be a real problem for the French if they wanted to deploy any. The snorting range of the Agosta is given as 8,500nm at 9kts, about half of the Oberon's range (15,500nm/8kt). The Daphnes at 4,500nm would be useless.
Surface Ships
Not every single ship could be sent with some in refit and others on other deployments but this is what theoretically the French could select from.
Clemenceau and Foch - both newly refitted and both with Senit 2 (taken from other ships), reliant on 100mm guns, air group of 16x Etendard IVP, 10 F-8E, 7 Alize & 2x Alouette (though doubtless more would be crammed aboard),
Jeanne de Arc - Exocet & guns, may well have still be in her planned 1982-83 refit and unavailable which would be a huge blow for both troop lift and helicopter provision without cluttering C&F
Colbert - CG, Mascura & Exocet & 100-57mm guns plus has some armour
2x Suffren - Mascura & Exocet & Malafon plus they have the DRBI-23 radar
Probably 1-2x Georges Leygues available - brand new, Exocet & Crotale plus Malafon and 2x Lynx each (note French Lynx is ASW only)
3x Tourville available - Exocet & Crotale (think all had it by 1982) plus Malafon and 2x Lynx each
Anconit - Malafon and guns
La Galissionneire - guns & 1x Alouette helicopter
Duperre - Exocet, guns, 1x Alouette
5x D'Estrees - Malafon & guns, no Senit, D'Estrees had a SCOT terminal though as experimental fit so might be able to make use of UK intel
4x Kersaint - Tartar SAMs & guns, some probably had DRBV-22 radar by 1982
Forbin - now a training ship but its a destroyer with another helicopter platform and guns and could be sent
8x Commandant Rivierre & Balny - most have Exocet but most lack the 30mm guns and have Bofors still
2-3x E-52 class - guns
D'Estienne D'Orves class - could be sent as additional escorts, can carry 17 (probably more) troops
Amphibious Warfare
Ouragan and Orage - LSDs, 350-470 troops, 2x EDIC or 18x LCM(6) each
5x Argens - LSTs, 1,800 tons or 170-807 troops, 2x ships have hangars for 2x Alouette each
2x Champlain - LSMs, 138 men & 12 vehicles each
Only 12 EDIC exist and 16x LCM (8) plus 11 LCM(3)
Support Fleet
Jules Verne - repair ship
5x Rhin - tenders
2x Durance - replenishment tankers
Isere - replenishment tanker
La Seine - replenishment tanker (think still operational in 1982)
La Charente - tanker plus fitted as a command ship
2x Punaruu - tankers
Saintonge - provisions ship
Plus other ships that could be press ganged into the task force
Henri Poincare - missile-range tracking ship, could be used as command platform at a push
Ile D'Oleron - Crotale and Exocet test ship
Berry - EW equipment trials ship
Triton - underwater research ship, could be used as a tender
Aunis - towed-sonar test ship, former transport so could be used as a transport
D'Entrecasteaux - research ship, could be used as troop ship, can carry 3x landing craft and has a helicopter platform
It's clear that any French task force would be smaller than the British task force (which was 43x RN, 22x RFA, 62x merchant) and so would rely on merchants for additional transport tonnage. The replenishment fleet looks pretty thin given some of the French ships have short range plus there is no backup from Ascencion.
The amphibious fleet isn't too shabby and broadly comparable with the RN's but would need assistance from commercial ships for lift, especially heavy lift.
The combat fleet is patchy - a lot of 1950s retreads and some newer destroyers - only 7 SAM ships plus 5 destroyers with Crotale - ironically the French have exactly the reverse of the RN, a lot of ships armed with SSMs and ASW missiles but few AA platforms. Ship-borne helicopters probably limited to 10 Lynx and a couple of Alouettes on the destroyers ignoring any transport types on Ouragan and Orage and if Jeanne d'Arc is in refit its a serious loss.
It's a big gamble, could the French do the same with up to 1/3 less ships? Fewer modern SAM ships and perhaps limited submarine escort (snorting all the way from Lorient they might be too late to do any good) but on the upside have two fleet carriers with decent airwings.
As to CIWS - well like the RN it's mostly 40mm Bofors and a lot of 100mm mounts which might prove quite handy. Nothing like Sea Wolf but Crotale is effective too. What is French EW like? presumably they know best how to jam Exocet.
Does the French admiral use his superior number of Exocets in a surface action supported by carrier air?
The Belgrano southern wing won't be sunk by an SSN so its possible it might come to reliance on missile power. I think freed of any SSN threat the De Mayo will be out and a danger once the fog clears and the wind picks up enough to launch her aircraft.
Interestingly Flottes de Combat 1980/81 claims for De Mayo "The British Sea Harrier V/STOL attack aircraft is to be acquired to augment the A-4Qs carried"....