I retrieved some old notes I have regarding the facilities available in the French Empire in June 1940.
(sadly it's a text without reference, and I can't remember where I found it, so I cannot guarantee it's 100% accurate).
Four drydocks : one BB-sized (255m*40m*12m), two cruiser-sied (203m*30m*9.5m) and one smaller (92m*15m*4.4m).
Mers El Kebir :
no drydock (two BB-sized were planned to be built in 1942-44).
Two small drydocks at Oran (civilian harbor)
Two drydocks in the civilian harbor (138m*26m*8.5m and 80*22*6)
one drydock, able to accomodate cruisers (198 m long).
One floating drydock evacuated from Bordeaux (??unconfirmed??
one BB-sized drydock was scheduled, apparently it was never built. It is unclear whether the work had begun before June 1940.
Four drydocks: two 150m*25m*9m and two smaller (<100m long)
French West Indies :
Fort de France (Martinique) :
One CL-sized drydock at least (Emile Bertin drydocked there in 1943, and no work on the facilities during 1940-43)
French Indochina :
Unkown, but most probably at least one drydock able to accommodate a Tourville-class cruiser
@ Jon :
Regarding the Malta Floating drydock, here is what I found on http://www.worldnavalships.com's forum :
The AFD in Malta was AFD-8 this was originally a German floating dock, taken over by Britain after WW1. A new mid section was built at Chatham in 1924 increasing its capacity to lift 65000 tons. The original German dock left Sheerness on 1 June 1925 in tow of RETORT, RESOLVE, ROYSTERER, ST CLEARS, ST DAY, ST MELLONS. It arrived at Malta on 27 June. The new section left on 1 Aug 1925 in tow of RETORT, RESOLVE, ST CLEARS, ST MELLONS, ST KITTS, arriving 22 Aug. The sections were then joined at Malta. This dock was obviously capable of docking any size of RN battleship. Unfortunately the dock broke apart and sank after near-misses from Italian bombs in late June 1940.
Here again, sadly, I have no idea of the primary sources.
But looking through Hood's logs (on hmshood.com), I found that she had drydock periods at Malta in 1937-38. I've not been able to confirm that it was the AFD 8, but it nonetheless proves the availability of a BB-sized docking facility in Malta by that time.
03–27 February: At Malta. Taken in hand for docking, 03-13 February.
10–30 September: At Malta for dry-docking
06 November–31 December: At Malta (06 November 1937 - 05 January 1938). Taken in hand for docking, 08 November - 16 December
07 May–28 June: At Malta in preparation for the Summer Cruise of the Mediterranean Fleet. Taken in hand for rearmament and docking, 16 May - 22 June
09 November–31 December: At Malta for docking and repairs (09 November 1938 - 10 January 1939).