WI: John, Duke of Bedford marches south after the Battle of Verneuil?

While browsing Wikipedia, I came across the article for the Battle of Verneuil under it's "On this day". Curious, I read the article, then in the "Aftermath" section, I found this:

"Dauphin Charles was forced to postpone his plans of coronation at Reims. In the aftermath of Verneuil, the road appeared to lie open to take Bourges and thus bring all of France under English rule.[29] Bedford, much inspired by the example of his late brother, Henry V, preferred to concentrate on finishing off the job of subjecting Maine and Anjou rather run the risk of leading an advance into the south of France with these two provinces only partially conquered.[29] Bedford preferred to methodically conquer one province at a time rather than risk all on a bold drive to conquer the south of France in one campaign, which might finally bring all of France under English rule, but which equally might end in disaster.[29]"

I'm not sure if it's entirely accurate, but what might have happened if Bedford had marched south after the battle?

Any thoughts?
 
I think either he risks being hit from the rear, unless his lieutenants are good, or, he can somehow force a confrontation with Charles and end things once and for all
 
As he thought it's a high stakes gamble. Best case as VVD says Charles offers battle and it's all over. But the odds of that are very long. After Agincourt and Verneuil the French rightly avoided battle apart from when the odds were massively in their favour or they didn't have a choice.
So in all likelihood Bedford effectively does a massive unopposed chevauchee (like the Agincourt campaign) and returns to the north with a load of loot and settles down to securing those bits that aren't under his control like OTL. Plus side southern France is more devastated while his coffers are fuller. Downside some of his troops will go home to spend their loot and the French garrisons in the north have more time to prepare.
Net effect: minimal.

Bedford's strategy of systemically securing France and trying to make the entire thing self funding was the right one, it's just the odds were too long and Charles too smart.
 
As he thought it's a high stakes gamble. Best case as VVD says Charles offers battle and it's all over. But the odds of that are very long. After Agincourt and Verneuil the French rightly avoided battle apart from when the odds were massively in their favour or they didn't have a choice.
So in all likelihood Bedford effectively does a massive unopposed chevauchee (like the Agincourt campaign) and returns to the north with a load of loot and settles down to securing those bits that aren't under his control like OTL. Plus side southern France is more devastated while his coffers are fuller. Downside some of his troops will go home to spend their loot and the French garrisons in the north have more time to prepare.
Net effect: minimal.

Bedford's strategy of systemically securing France and trying to make the entire thing self funding was the right one, it's just the odds were too long and Charles too smart.

Charles or Marie of Anjou? Charles always struck me as an incredibly fortunate man aha
 
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