Would he have gone to Paris personally or sent (say) Secretary of State Elihu Root to negotiate?
If the latter, I can just see Woodrow Wilson's argument as he seeks his comeback in 1920 (without the strain of being president in 1919 we'll assume that his stroke is butterflied away): "No wonder the peace treaty is so full of injustices. The president failed to use his personal prestige to fight on the scene for a fairer treaty. *I* would have gone to Paris personally..." and a lot of voters would agree with this, "yeah, if the president had just gone to Paris personally, it would have been hard for Clemenceau and Lloyd George to resist his proposals..."