There are many different possibilities:
Assuming the whole dynamic that led up to the rise of Hitler still happens, it makes the dance between Hitler and the western democracies different. France wanted to respond a little more aggressively at times to Hitler but was completely unwilling to do anything without British approval. In TTL, there is now a third party, the US, that France can look to for some kind of signal of support. The US is probably still pretty isolationist and not real inclined to go on crazy adventures, but with three parties instead of two, and with the US still being at a bit of distance, there is more room for communication errors, ambiguities, personalities, and the ins and outs of diplomatic maneuvering to lead France to, perhaps mistakenly, think it has the go ahead from its allies at some point. If nothing else, France may be a bit more confident with the expectation, perhaps not wholly accurate, that the US has her back.
That was the era when diplomatic agreements were taken quite seriously. So even though the US will still be quite isolationist, I expect not quite as total of a draw down of the military long term and not quite as much disinterest in the increasingly dangerous European situation in the 1930s. Pacta sunt servanda. It will provide Presidents and Secretaries of State more room for maneuver. If nothing else, they can always explain that their attempts to meddle in European affairs are efforts to stave off a war "into which our commitments could draw us in." Membership in the League, even without Article X, will also give the US more involvement in what is going on in Europe.
The presidential dynamic is different. As pointed out upstream, swapping a Republican for a Dem at this point probably shakes up future presidential elections. President FDR probably doesn't happen OTL. The President is probably still an internationalist of some kind, but perhaps in a different way with different prejudices and different political necessities than FDR had.
Anti-appeasers like Churchill may have a stronger hand if they can draw on a broader confidence than OTL that the US will come in on the British side.
The US never quite embraced the post-war guilt thing that the British and the French did. They may be less willing to whitewash over Nazi nastiness from a feeling that they deserve it.
An interesting possibility where greater US involvement might actually make some: if history develops somewhat similarly to OTL up through Czechoslovakia, France and Britain may be less willing to give a guarantee to Poland without US involvement. They won't want to commit themselves to a war without the US, because in TTL they are relying on the US, so any action that might give the US an excuse to say that they have brought a war on themselves that relieves the US of its treaty obligations would be something to avoid. OTL, the guarantee to Poland specifically was a bit random. TTL, I'm not sure the Americans care much about Poland per se or have quite reached the level of outrage yet that the British public reached after Czechoslovakia. Maybe there is no guarantee or tripline set up until after Germany has knocked off Poland in cahoots with the Russians.
Lots of possibilities to play with.