Assuming that forces and industrial capacity were similar to OTL I would say very unlikely simply because the former bloc would be so much stronger than the latter.
It would depend on the details, for instance does the western operations start with a massive German attack on France via Belgium or is it on the defensive against France while committing its main forces against Russia in support of Austria?
In the former case with France having to consider threats from Britain, including blockade as well as possible landings, and Italy France might fall or be so badly weakened its shortly required to make peace. Especially if as OTL its loses its primary industrial area and can't rely on imports from allies and neutrals because Britain is now an enemy preventing both. Similarly Russia can't rely on western industrial supplies - albeit limited - or finance from Britain.
In the latter then Russia is in for a lot of grief although they might well trade space for time. France faces blockades and possible attacks as well as the whittling away of their imperial empire while its own attacks on Germany or Italy are likely to be very costly.
Coupled with American isolationism and that Britain can now rely on Germany to supplement its own industrial/military needs and supply the latter with raw materials, food and funds I can't really see anything that would drag it into the conflict. Unless as WolfBear says France tries USW in which case there's a chance if the war lasts long enough the US ends up against France which tilts the odds even more against them.
