It took me time but I will answer your point:
The French didn’t panic, they had a plan: in November 1939. Gal..Gamelin knew that most probably, the Germans won’t respect Holland and Belgium neutrality. As soon the German will cross the borders (belonging to a democratic country, you can’t put yours troops on their territory without their agreement, that the answer on one of your remarks), the Allies will go on the Dyles river, making possible a short front line, a protection of the coal mines of Hainaut and Borignage. In December, Gal Georges and Gamelin decided that parts of the 7th army will go on the Escault to join with the Dutch forces in Breda. The plan has his flaw, but nothing indicates a panic from the French side.

About the reinforcement proposed by Churchill, we have three account of the meeting when the French told Churchill that they will ask for an armistice. De Gaulle, Petain and Churchill wrote about it. De Gaulle wrote that Churchill reminded Petain that in March 1918, during the battle of Amiens, he succeeded to win the battle. Petain then answered “Yes, but I sent 40 divisions to rescue your troops. Where are you 40 divisions?” Edward Spears, Churchill’s personal emissary noted that the “lyric description of Paris collapsing on its heroic garrison refusing the defeat” didn’t appeal to the French Generals. Weygand even added that to transform Paris in a field of ruins won’t change the end. 11 days after the fall of Paris, the French army was still fighting.

So, can you ask your Magazine where they find this information? Honestly, a division wouldn’t change a thing. The Germans tactic wasn’t to fight, but to avoid the contact, and to cut the other army in small pieces they will finish later.

I know I won’t succeed to change you opinion. But, if you read REAL history books, you will find, as I did, that not only the French fought, but they fought bravely. The proof: the Gal Waeger gave the Honours of the War to the French defenders of Lille.