Very difficult with de Gaulle remaining in charge of the Free French.
Instead, get the Interior Minister Georges Mandel and Defence Minister (and former Prime Minister) Edouard Daladier to Britain, rather than North Africa. Cesar Campinchi and the Minister of State, Louis Marin would also be useful. These men were all leading 'hards' in the French cabinet at the time. Campinchi would have been able to issue orders to the French Fleet with at least some confidence of outweighing the orders issued by Darlan.
None would have equaled the prestige of Petain, but they all had more political prestige, clout and public profile than de Gaulle had, with the possibility of more colonies and men joining the Free French cause from the outset. Daladier in particular, could have used the dissolution of the French parliament on July 10th and Petain’s assumption of the presidency to denounce him and declared that he, as most senior remaining member of a legitimate French cabinet sworn in by President Lebrun, was assuming the duties of the premier and leading a French Provisional Government in Exile.