Wilson was an idealist,and wanted a "peace without victory" (whatever that meant) that basically wasn't going to punish Germany for losing a long and destructive war which they had been chiefly responsible for starting. This would make Wilson look the big international peacemaker,and the great international statesman on the world stage.
However,France and Britain had done most of the fighting (and therefore the dieing) in WW1 on the Allied side, and so weren't prepared to just sit back and let USA - which hadn't even joined the war until well into 1917 - dictate the subsequent peace treaty,especially one that didn't punish Germany.Additionally,many of Wilson's Fourteen Points,that he wanted to base the treaty wholly on,were unacceptable to Britain and France.