If Britain does sue for peace, papa Joe is gonna be looking pretty smooth, as being the guy that predicted they would fold and that the U.S. shouldn't get involved. And the real life guy waiting in the wings to run in 1940 if FDR didn't run for a third term, which according to some posters here on these boards he wasn't going to do if there was peace in Europe, was political machinist turned Postmaster General James Farley, also an Irish Catholic.
So Joe winning is probably up to chance, even with the OTL landslide victory of FDR against Landon, but considering the OTL candidate if FDR didn't run for a third term was going to be an even shadier Irish Catholic than Kennedy, it is consider it implausible.
And Roosevelt was planning prior to Pearl Harbor to lift the trade embargo with Japan, so if things start looking more dangerous in the world, that plan could quite easily rise to the surface earlier and be transmitted to any chosen successor.
Detaching Japan from the Anti-Komintern Pact shouldn't be so hard in terms of a temporary measure. All it takes is selling them oil again, I've been led by the information to believe. And Britain could, if it had peace, do that if the U.S. does not.
What is going to complicate the West's relationship with Japan is the Japanese invasion of French and Dutch Pacific colonies. Japan might stay off of British and U.S. territory temporarily if both those nations are at peace and thus not vulnerable and are trading with them as normal, but unless both countries are willing to just ignore Japan preying on the weaker Pacific colonial empires there are going to be problems quite quickly after a June peace along the Fletcher Saltoun model in his timeline that was linked.
Of course, if the anti-war faction who blame the war for the loss of territory or militarists who blame the government's surrender for loss of territory win power or seize it in France, that could give Halifax an excuse to ignore whatever trouble France gets into. And who knows, the Dutch East Indies and French Indochina might whet the Japanese military's need for raw materials enough, especially if Germany pulls an earlier Barbarossa due to peace in the West. Even formally detached from Germany thanks to a British or American bribe of lifted sanctions isn't necessarily going to stop Japan from kicking the Soviet Union while it is down, declaring a separate war on it (thinking of the war as multiple different wars was how Spain rationalized its weird international political position after all) to invade the Russian Far East.
Or Britain, the United States, and France could beat the crap out of Japan while Germany is eviscerating an ill-prepared and not-getting-lend-lease Russia.
Also, I think rather than British troops stationed in France to get by post-WWI troop limits imposed on France in the peace as Fletcher has it in his timeline, maybe if the wording of treaty is to continental France, France would mobilize additional troops and build/move military infrastructure beyond the treaty limits in the colonies.
So maybe something like this...
Halifax instead of Churchill on May 9th/10th
Successful evacuation of Allied troops cut off on the North French coast in early June, followed swiftly by a request for ceasefire. Then the peace treaty is hashed out, with peace by the start of July.
Walking into the Democratic convention in July with peace in Europe, FDR is pressured (quite big pressure OTL already) to not run a third term and can't justify one. Though Farley wants it, finagling and negotiations in the Democratic Machine faction land on Joe Kennedy, the ambassador to Britain who predicted the peace. Joe is considerably less tainted with political corruption than Farley or the other New York and Chicago Machinists.
Britain is under no obligations by the treaty regarding arms and troops, and begins military build-up. France circumvents treaty and checks future aggression from the concessions, likely in Tunis, it gave up to the Axis in the peace by building up its troops and war industries in remaining colonies like Algeria and West Africa.
Japan's Pearl Harbor ITTL is not being willing to change its invasion plan of French Indochina in July in order to embargo oil imports into China, even though France and Britain are now at peace with Germany. Germany can't pay attention to their Far East frenemy, because they're rapidly shifting their forces for a much sped up sneak attack on the Soviets.
What follows is a British-French (and colonial Dutch) fight against Japan, with newly elected Joe P. Kennedy Sr...selling to both sides? And thus establishing an Anglophobic stance to the isolationist wing of the Democrats, now in ascent. The Brits have no love lost for the guy regardless and there's no point predicting that the U.S. is better off not joining in the early war against Germany due to Britain being likely to fold only to them get in a war with the Japanese, so bribing them with a lifted trade embargo to focus on other things before turning their eyes to the Philippines is not unreasonable.