Popular understandings of the Fall of France seem to focus almost exclusively on the encirclement of Dunkirk and the destruction of the Allied forces in Belgium throughout late May, 1940. Yet the weeks during and following Dynamo were characterized by fierce fighting, and massive subsequent operations were required to breach French defensive lines on the Somme and to isolate the Maginot Line. Was the German success in Belgium decisive enough that these operations could be characterized as 'mopping-up,' albeit on a massive scale, or was the fate of France only decided in subsequent battles East of Paris?
The Allied condition was dire after Dunkirk. Prior to the initial attack in the West (Fall Gelb) both sides had roughly equal strength, somewhere in the neighborhood of 150 available divisions. At the start of Fall Rot the French had 64 divisions remaining and the British had 1. Compared to this the Germans had 142 divisions ready for immediate action.
What's worse is that the Allies had lost an enormous amount of material. They had lost heavy guns, armor, planes, trucks, and more, a large amount of which had been captured by the Germans. The British and the French had men available. What they didn't have is any equipment for them to use.
That sets the stage. The Germans were in good shape. Casualties had been relatively light. Supplies were plentiful. The men were in a high morale. The units were organized and in positions. They also had a 2-1 advantage in the coming fight. The French were in terrible shape. Casualties had been high. Supplies were stretched. The men had low morale. The units were disorganized and had been recreated in an ad hoc fashion, and they were sitting (in many cases) in unprepared positions. The Germans also had almost complete control in the air.
At the time it was reasonable to assume that given some time the French would be able to restore rough parity and that the BEF would be reconstituted and redeployed into France. I personally wouldn't characterize the first week of Fall Rot as a mopping up scenario. The Germans had the French in the ropes, but a rally was possible. But the Germans hit the French hard and fast enough that they weren't able to rally. Once Paris fell I would characterize it as a moping up operation. The Maginot line was isolated from the rest of the French Army, which was in full retreat with no clear rallying point. But until the 14th the issue was still in doubt, if highly favorable toward the Germans. After the 14th it really wasn't in doubt any more.