From Wiki:
Allied strategy
…
In September 1939, in the token Saar Offensive—only made to nominally fulfill the prewar guarantee to Poland to execute a relief attack from the West—French soldiers advanced 5 kilometres into the Saar before withdrawing in October. At this time, France had deployed 98 divisions (all but 28 reserve or fortress divisions) and 2,500 tanks against German forces consisting of 43 divisions (32 of them reserve divisions) and no tanks. According to the judgment of Wilhelm Keitel, then Chief OKW, the French army would easily have been able to penetrate the mere screen of German forces present.[14]
After October, it was decided not to take the initiative in 1940, though important parts of the French army in the 1930s had been designed to wage offensive warfare. The Allies believed that even without an Eastern Front the German government might be destabilised by a blockade, as it had been in the First World War. In the event the Nazi regime would not collapse, a possibility that seemed to grow ever more likely,[15] during 1940 a vast modernisation and enlargement programme for the Allied forces would be implemented, exploiting the existing advantages over Germany in war production to build up an overwhelming mechanised force, including about two dozen armoured divisions, to execute a decisive offensive in the summer of 1941. Should the Low Countries by that date still not have committed themselves to the Allied cause, the Entente firmly intended to violate their neutrality if necessary.[16]
Obviously the Germans might strike first, and a strategy would have to be prepared for this eventuality. Neither the French nor the British had anticipated such a rapid defeat in Poland, and the quick German victory was disturbing. Most French generals favoured a very cautious approach. They thought it wise not to presume that the German intentions could be correctly predicted. A large force should be held in reserve in a central position, north of Paris, to be prepared for any contingency. Should the Germans indeed take the obvious route of advance through Flanders, they should only be engaged in northern France, when their infantry would be exhausted and they had run out of supplies. If however they would try an attack on the centre of the Allied front, this Allied reserve would be ideally positioned to block it. If the Germans advanced through Switzerland, a large reserve would be the only means to deal with such a surprise.
Dyle Plan
Gamelin rejected this line of thought, for several reasons. The first was that it was politically unthinkable to abandon the Low Countries to their fate, however prudent it might be from an operational point of view. Certainly the British government insisted that the Flemish coast remain under Allied control. The second reason was that the 1941 offensive had no chance of being decisive if it had to be launched from the north of France against German forces entrenched in central Belgium. The German offensive had to be contained as far east as possible. The last and for him personally most cogent argument was that Gamelin did not consider the French army capable of winning a mobile battle with the German army. The French infantry divisions as yet were insufficiently motorised. The events in Poland helped confirm his opinion. Such a confrontation had to be avoided at all cost, and Gamelin intended to send the best units of the French army along with the British Expeditionary Force north to halt the Germans at the KW-line, a defensive line that followed the river Dyle, east of Brussels, in a coherent tightly packed continuous front uniting the British, Belgian, and French armies. This plan thus presumed that the Germans planned to concentrate their forces where they could be well supplied by the better road network of northern Belgium.
Gamelin however did not have the personal influence to simply impose his will. The first step he took was to propose the “Escaut” variant as an option for Plan D — the codename for an advance into the Low Countries. It was named after the river in Flanders. This was a shrewd move: protecting the Flemish coast seemed the least one could do; on the other hand it created an enormous salient, showing that it made more sense to defend along the shorter Dyle line, which was precisely the content of Gamelin’s next proposal. This however was too transparent. His second “Dyle Plan” met with strong opposition, not growing any less when the 10 January crash confirmed that the German plans conformed to Gamelin’s expectations. Also Lord Gort, the commander of the British Expeditionary Force, was beginning to expect that whatever the Germans came up with instead would not be what he had initially predicted. The main objection was that the manoeuvre was very risky. The Allied forces had to complete their advance and entrenchment before the Germans reached the line, for which there seemed to be too little time. When entrenched they would have trouble reacting to German strategic surprises, also because their fuel supplies would have to be replenished. The next problem was that this line was very vulnerable to the German main strength, their large tactical bomber force. Nothing seemed to prevent them from breaking the line by a massive bombardment, forcing the French Army to an encounter battle after all.
…
Well? Would it have worked? Could the Allies have achieved strategic dominance in a war of attrition and successfully invaded Germany had the Battle for France never taken place in 1940?