Why wouldn't there be an Axis if the CP still loses despite Sweden's involvement?
Assuming it still loses despite Sweden's involvement? (which is rather difficult to do)
Swedish involvement is going to draw the war out longer, meaning the Entente is going to be more vengeful, not necessarily France, but the US and UK who will suffer the vast majority of the extra casualties. They are going to be less willing to moderate France's demands at the Peace Table and more willing to back her up later when she tries to collect. France wanted to knock off Germany the second Hitler remilitarized the Rhineland, the UK refused to back them and it didn't happen. UK backs them WWII never happens, hell the Axis never happens
Or they could decide to go whole hog at Versailles and Balkanize Germany to the point where it can't become the threat it became OTL
Plus there is the probability that the US and UK are pissed off enough to drive over the Rhine, which gets rid of the stab in the back myth the Nazi's made much hay over