Then the Germans were screwed. Maybe. The fate of the war would then be decided in how quickly the French command reacted and the plan.
My thinking is that beyond some very limited counter-attacks, there would be no concerted push to drive the Germans back, and possibly even continue on to Berlin like in 44-45. The BEF wasn't in the right place and the French had based their military, strategically and tactically to fight defensively.
Added to how ponderous French high command was back then (they didn't have a Rommel or a Patton who would just jump in a tank, shout 'follow me!' and go for it without express orders to do so), I think by the time a plan had been created, filtered down to the corps and divisional commanders, units moved into place, artillery repositioned etc, the Germans would be in place to block said attack (mostly using tactical air power rather than tanks) and you'd end up in that kinda stalemate that birthed the trench warfare of WWI.
It'd be an interesting political situation. Germany has no interest in a protracted war at this point. France and the UK are in no position to willingly finance another war. The USSR probably wouldn't push for continued hostilities as it stands to gain nothing that far west and also isn't ready to assist Germany (they're still allies at this point) in a protracted trench fight.
Possibly Hitler could wangle a stalemate, bilateral de-escalation, maybe hand back Czechoslovakia as reparations. Even that would depend on the Allies ability to enforce such things.
In the end, what the french army really lacked was some skilled generals (and we were considered the best army in the World then...
).
However, a possibility I thought about is that, while the germans and the allies more or less neutralized each other, the russians could have built without being bothered an army strong enough to steamroll Europe in a few years. That was actually what Stalin planned, he wanted to save time, but he thought that the french and the british would hold the germans a bit longer than that...
Also, the italians would probably have not involved in the conflict then (they only declared war on France when it was closed to be defeated). Spain would have certainly stayed neutral too, for the same reason (the country was devastated by the civil war that happened in 1936).
If the school teacher had told the dictator 'no, you're not getting a free country', like he should've done?
I don't think it would've changed much. Hitler wanted the land, and betted that the Allies were too weak to actually stop him. He might have invaded Czechoslovakia anyway and taken it illegally.
Or held off a year or 2 and invaded France/Russia like he was always going to. Personally I'd have gone for Russia first. Invaded Poland in the march of '40 with the USSRs 'help' and then continued east straight through the Red Army and used all the spring/summer of 1940 to tear the USSR to pieces whilst the Allies are dithering about wondering what is going on during the so called 'phoney war' on the western front.
Then either make a deal with the Allies to stop there now he has his living space (a not so difficult sell considering the Allies are no fans of the communists either, added to the previously mentioned lack of finance/political will for a war in the west) or re-deploy after clearing out Moscow and crack on with blitzkrieging Europe as planned.
Yep, basically the war would have started in 1938 then. And Czechoslovakia would have been steamrolled for sure. But it would have probably been harder for the nazis overall. Because in 1938, with the Munich agreement, Hitler seized some high quality military material (tanks especially), which we regreted a lot one year later...
But if war started in 38, he wouldn't have had those tanks. The allied would have probably not attacked much though, and we would have had another phoney war. And the russians would have probably not helped too. Stalin wasn't invited to Munich, so he didn't participate in the decision process, and he really had no reasons to come and help the allies. Anyway, his country was separated from Germany by Poland, which was very good like that. This gave him time to prepare himself.
On another side, the non agression pact didn't happen at that time, so Hitler would not benefit from russian deliveries, and the naval blocus held by the Royal Navy would have paid off. Because of this, Hitler probably couldn't have invaded France like he did. And if it didn't happen, he would have probably not declared war on Poland and then the USSR, as he can't afford a 2 fronts war.
But as the allied army wasn't oriented towards offensive, they would have not been able to attack either. I don't know how this would finish (the allied would probably ask help from Stalin, which he would hardly accept if he does), but this would certainly last a lot of time...
Hard to say how it would have happened, but sometimes I think that we actually lost the war in 1938...