Which part of this historical paragraph is NOT true?

During World War II, Franco refused to allow German troops to cross Spain to attack Gibraltar. Laval wanted the French Air Force in North Africa to work with the Germans. Petain had Laval arrested on December 13, 1940. From August through November, the Germans lost over 2,000 planes. This allowed Britain time to rebuild its land forces. Hitler then decided to attack Britain's lines of communication with the British Empire. The German Air Force began to attack the RAF in the summer of 1940. In spite of the fact that the British Spitfires were not as good as the German Messerschmidts, "radar" gave the British the advantage. The German and Italian forces occupied all of France in November, 1942, after the landing of Allied forces in North Africa.