From what is publicly known and of which I am aware, I think the story goes like this.

Branson never even thought about asking for the AF machines until the end of May, about 4 or 5 days before AF stopped flying.

The reason? Because he was not really that serious about flying Concorde per se. All he wanted up until about then was a chance to gain positive PR for himself and for VS at BA's expense.

What changed? Branson met Airbus to put to them his financial proposals for operating the aircraft. From the tone of what was said by the two sides afterwards, Airbus listened politely. I believe that Airbus also told him what the economic realities were for anyone who wanted to be the only operator in the world of a fleet of 7 aircraft (as opposed to being one of 2 operators of a total fleet of 12), and why AF's retirement decision was truly the reason why BA's operation was going to become uneconomic. (Or, to put it shortly, that BA was telling the truth about why it was also retiring its fleet.)

Branson's response? That day, or thereabouts, he wrote to Spinetta asking to buy the AF machines. About 6 weeks too late - AF's museum promises and plans were already made, done and dusted. Of course, AF might have been unwilling to do it anyway, but any chance that Branson might have had on 10 April was lost by his own inaction.