If both Britain and France didn't try the convoy, but instead made the attacking move directly with their fleet, BOTH MOVES WOULD SUCCEED (ie, French fleet is now in Gibraltar and British fleet in Mid Atlantic after Gibraltar successfully bumped Spain). However, if they both convoy, it is impossible for both to succeed, but also impossible for both to fail.

I have not eyeballed the map and plotted things out, but my head is starting to hurt, so there may well be a convoy paradox here.

The primary issue here is that standard diplomacy doesn’t have convoyable canal territories, like Gibraltar in 1900.

Here is a somewhat similar situation that I’ve come up with in standard diplomacy - there is a distinct difference, but it may give insight into what happens in your scenario:

Italy has a fleet in Western Med and an army in North Africa. France has fleets in Mid Atlantic and the south coast of Spain. Italy attempts to convoy from North Africa to Spain, through Western Med. France moves to Western Med from Mid Atlantic, supported by Spain. Does the convoy reach Spain and cut its support? Or does the supported move to Western Med take precedence and break up the convoy?

I believe that Italian convoy should fail, as the support from Spain dislodges the convoying fleet in Western Med “before” the army reaches Spain (though of course orders process simultaneously in theory). That would also lead me to believe that in your scenario, the Gibraltar fleet is dislodged and the French convoy is successful.

Of course, the key difference between the scenarios is that in 1900, both moving pieces are convoys, and the English convoy is attempting to cut a support hold rather than a support move. In standard diplomacy, the result would be similar to the idea that since a unit cannot cut the support of an attack upon itself, a convoyed army cannot cut the support of an attack upon its convoying fleet. Whereas it’s much more reasonable to believe that a convoyed army could cut a support hold on a convoying fleet whose convoyed army would otherwise dislodge its own convoying fleet. I think you’d have to play test this scenario to be certain either way.

It is the basest form of convoy paradox. vDip would adjudicate it by making it a standoff with everybody stuck in place.

Let's sort it out on the real thing! Last chance:
Paths of Glory
https://www.vdiplomacy.com/board.php?gameID=57690

Since GIB is unsupported and WMED’s support is not cut, doesn’t the French move dislodge GIB since the British convoy can never go through to cut SPA’s support over a dislodged fleet? I.e., nothing ever dislodges the French fleets making the French convoy. But if there’s support on GIB, then there would be a convoy paradox?