[vkou]

The British expeditionary force was tiny, and the Russians were smashed. Neither could have fought on in Europe after France was eliminated.

Unlike WW2, it was also not an existential war - it was just another European conflict. An armistice gets signed, the losers pay reparations, everybody goes home.

[WesleyLivesay]

I think the comment above is questioning the belief that France would have packed it in and called it a day if Paris was captured (I believe the answer is no) not what would have happened if France was out of the war.

[vkou]

In that case, they underestimate the importance of Paris as a center of bureaucracy, logistics, communication, as well as that of the fortifications between it and the border.

France may have been able to hold on for a while longer, but losing Paris would have almost certainly made an armistice the preferable option. It would not have been able to regain its territory, its industrial output and manpower would have been dwarfed by Germany, and its allies were in no position to offer assistance.