The point is the the UK declared war first, by some hours. Both the Right and the Left in France were demoralized, but linked through traditional alliance with the UK. Yes, the French Right had wanted to fight but felt that the British had sold them out at Munich, whereas the French masses wanted peace - as they did in June 1940 once France's armies were routed.But actually the UK and France both declared war against Germany on 9/3/1939. Suchender says that France invaded immediately and had some quick successes before abruptly halting their forward march. So your theory would explain why the French stopped their attack, but not why they started it in the first place.
FWIW, the WishyWashyPedia says that this period was known as the "phoney war", based on the comment of US Senator William Borah, who said "There is something phony about this war." A sentiment I'm sure we all can agree with. The editors go on to explain:
The offensive in the Rhine river valley area started on 7 September, four days after France declared war on Germany. Since the Wehrmacht was occupied in the attack on Poland, the French soldiers enjoyed a decisive numerical advantage along their border with Germany. Eleven French divisions advanced along a 32 km (20 miles) line near Saarbrücken against weak German opposition. The attack did not result in the diversion of any German troops. The all-out assault was to have been carried out by roughly 40 divisions, including one armoured, three mechanised divisions, 78 artillery regiments and 40 tank battalions. The French Army had advanced to a depth of 8 km (5.0 miles) and captured about 20 villages evacuated by the German army, without any resistance. The half-hearted offensive was halted after France seized the Warndt Forest, 7.8 km2 (3.0 sq mi) of heavily mined German territory.On 12 September, the Anglo-French Supreme War Council gathered for the first time at Abbeville. It was decided that all offensive actions were to be halted immediately as the French opted to fight a defensive war, forcing the Germans to come to them. General Maurice Gamelin ordered his troops to stop no closer than 1 km (0.62 miles) from the German positions along the Siegfried Line. Poland was not notified of this decision. Instead, Gamelin informed Marshal Edward Rydz-Śmigły that half of his divisions were in contact with the enemy and that French advances had forced the Wehrmacht to withdraw at least six divisions from Poland. The following day, the commander of the French Military Mission to Poland, General Louis Faury, informed the Polish Chief of Staff—General Wacław Stachiewicz—that the major offensive on the western front planned from 17–20 September had to be postponed. At the same time, French divisions were ordered to withdraw to their barracks along the Maginot Line, beginning the Phoney War.
Hitler was now the Soviet Union's ally, thus many French soldiers of Leftist persuasion would not want to fight Nazi Germany, hence France's half-hearted response, both at the top and among frontline soldiers. Britain soon became aware of France's lack of enthusiasm for war, so Churchill, when he became PM offered France "national union" with Britain in order to try to keep France fighting the Nazis. More sensible Frenchmen like Petain realized that a surrender and treaty were the correct way to go.