Assume the Allies do attempt to land on France without taking North Africa first (I think this was the British idea but the Americans ruled it out). IOTL the Germans occupied Vichy France in response to the French surrender in Algeria, but here there is still an 'indepedent' French authority when metropolitan France is invaded. Could Vichy France declare war on the Allies?
The Americans wanted to go the direct route from the very first moment they entered the War, the British didn't think the Allies were capable of doing this until the Mediterranean was secure.
The British were right in that neither the material nor manpower was available for a cross-channel invasion until 1944 and going through North Africa and Sicily provided vital experiance in both actual combat for the Americans and coalition warfare for both parties - in fact the invasion of Sicily was to provide many lessons which would make the invasion of Normandy a success - and taking southern Italy allowed the Foggia Air Fields to fall into Allied hands which in turn gave them a base to strike at Nazi-Controlled central and southern Europe with the added bonus of forcing the Axis to transfer hundreds of thousands of troops from both Normandy and the Eastern Front to garrison the entire Mediterran coastline.
Alan Brooke and Churchill never outrightly opposed the cross-channel invasion and Brooke freely admitted the necessity of it. The only issue that split the Allies on the cross-channel invasion was
when to do it.
The Torch venture, however, was undertaken more through political necessity than a concensus of military thinking. Having declared war on Germany, and committed himself to a Europe First strategy, Roosevelt needed to get the American troops into action to appease his voters an if there was no concensus on the suitability of a cross-channel invasion in 1942 and no likelihood of the operation being undertaken until 1943 at the earliest then the Allies would have to turn their attentions eslewhere.
That Roosevelt was not-so-secretly fond of the North African venture anyway was a widely known fact amungst the American Chiefs of Staff, and it was a strong fear that Marshall harboured that should Churchill get hold of Roosevelt on his own he might sway the president into openly supporting the operation and diverting the Allied attention away from the cross-channel operations.
Marshall fought hard against the North African operation and, ironically, found himself an ally in the form of Brooke, who agreed with Marshall that the TORCH operation would reduce the amount of reinforcement available to the 8th Army with possibly disasterous consequences (this all occured slightly after Rommel took Tobruk and the 8th Army was in retreat to El Alamein), that it would result in thinning the Naval presence in other theaters especially in Aircraft Carriers and escorts, that the unknown factor of the French reaction to the landings made it a seriously risky business, that it would slow down the build up of troops and supplies in Britain for the cross-channel invasion to come and that it would dilute the Allied strenght rather than concentrate it.
Why, then, if Brooke agreed with Marshall did he side with Churchill and Roosevelt when the two military chiefs met their political masters? Well, that was simple. Alanbrooke may have had reservations about the North African venture but he had even greater reservations about the SLEDGEHAMMER and ROUNDUP operations Marshall supported for the invasion of France.
More so than anything did Brooke appose the SLEDGEHAMMER operation because it was designed to be a "sacrificial" invasion to appease the Russians, made up of primarilly British troops. CIGS had no intention of making any such sacrificial offerings, and certainly he would not be swayed by the notion of appeasing the Bolsheviks, he hated them with a passion and was deeply suspicious of them - no doubt Stalin would have mocked the attempt anyway.
Roosevelt and Churchill knew that Marshall and Brooke did not agree on the plans for the cross-channel invasion and were deadlocked over the issue and therefore stated that they were in favour of an invasion of France and the Low Countries only if Marshall and Brooke could agree on a sound and sensible plan to use. In doing this they made it appear as if they were supportive of an operation they knew was not going to happen anytime that year. They were passing the blame for undertaking TORCH onto Brooke's shoulders even though they supported it far more than he did.