A bit difficult to evaluate in my opinion because of the incomplete state of the ships.
Jean Bart was never completed in wartime, and had to be fought with jury-rigged rangefinders and fire control stations during Operation Torch. I don't think that Germany would have the resources to dedicate to competing her if she was theirs, while the British would likewise lack the equipment to complete her, and any conversion project would be costly and might not finish in time for the war.
Richelieu is a very different story, and in a theoretical completed state, and assuming whichever side had her could produce the necessary ammunition, she would be a powerful asset overall. From an Allied point of view, she would add another 30-knot capital ship to the British fleet, something the British were in short supply of (the three battlecruisers, and then the 27/28-knot KGV's as they came into service). For the Germans, she's another long-range raiding battleship.
Her speed came in combination with good armor (at least in thickness, as not much is known about armor quality as I understand), but firepower is probably where the French battleships fall short. Although the relatively lengthy firing cycle (45 seconds) available to the guns shouldn't be of great consequence (due to rate of fire per gun usually being about 1 rpm in battleship engagements, especially given use of salvo fire), the fact that the turrets may easily become obscured if the ship has to turn away is a significant vulnerability, and perhaps worst of all would be the the dispersion issues that dogged the ship until 60-millisecond delay coils were fitted in 1948. Although cases of 'excessive dispersion' can be prone to exaggeration some times, in the case of
Richelieu, where spreads 1.4-1.8
kilometers are recorded, it would make effective gunnery extremely difficult if not impossible in my opinion.
That being said, with a 14-meter Triplex Rangefinder in her director
, surely her rangefinding abilities must have been superior than any other European battleship (barring fire control radars, of course).
For the British, I think she would be a very useful asset. My hunch would be that she would become part of Force H, as a fast intervention force for either the Atlantic (in the event of German heavy raiders) or the Western Mediterranean in the event of operations from the Italian fleet. One can only imagine, for example, the greater freedom Vice-Admiral Curteis might've had during Operation Halberd had he been taking
Richelieu and
Prince of Wales against the Italians rather than having to haul along the poor old
Rodney!
From an Axis perspective, I think her most likely fate (ignoring the obvious fate of Vichy control, as this is purely a hypothetical) if sided with the Axis would've been falling under Italian control rather than German, as the Kriegsmarine would've lacked the manpower to operate an extra 1550-man battleship, with consideration to all their own warships coming online in the aftermath of the fall of France. For the Italians, it would've been a considerably lesser issue - in fact, I imagine they would have very few qualms with placing one (or even both) of the rebuilt
Conte di Cavour-class battleships into reserve to help man a modern 35000-ton battleship (and/or simply never wasted the resources on resurrecting the
Cavour after her sinking at Taranto). It would've been easier for them to operate than for the Germans, and would be considerably more useful in regards to the limitations German battleships had on their ability to sortie.
Regardless of who got the ship, however, it would've been considerably time-consuming and resource intensive to get her into full operational status with properly training a crew, especially if they must rely on their own sailors rather than the French crew (which would likely be a bigger problem for the Axis powers than the British). For the Axis, the addition of another fuel-hungry battleship would also entail more problems than it would for the British.
All those considerations aside, against any of the modern European battleships classes (
Bismarck,
Littorio,
King George V), in a ship-to-ship fight I think she would stand as at least equal to any of them - if not for the extreme dispersion issues. This would hamper her gunnery far too much, and I cannot think that this would allow her to effectively engage any enemy targets.
Vittorio Veneto is a perfect example of this - the fire control system was easily capable of accurately engaging any of her targets in the Encounter off Gavdos, and her salvoes were well aimed for most of the engagement - yet she fired 91 rounds at ranges of 23-25 km (25150 - 27340 yards) and failed to score a single direct hit on the British cruisers because the dispersion of her salvoes was too great (likely due to poor quality in powder consistency, which doubled her dispersion from what it had been the previous year) - up to 500m! If such dispersion precluded hits in such an engagement, than dispersion easily 3x greater on the part of the French 380mm guns would make hitting largely impossible.