The former New Zealand international all-rounder has plenty of captaincy experience, having skippered Wellington for three seasons.
He will also run the team in the first two NatWest T20 Blast games of the season, while limited overs captain Eoin Morgan is away at the Indian Premier League.
Franklin will be captain until the end of August, when either Voges or fellow Australian Chris Rogers will return to Lord???s and take the reins.
Nick Compton will be Franklin???s vice-captain.
Middlesex???s Managing Director of Cricket Angus Fraser told the club’s website: ???We are very fortunate to have a number of players at the club that were willing to captain the 1st XI when Adam Voges leaves.
???James has plenty of experience and I believe his calm, mature and measured persona will make the departure of Adam as seamless as we can possibly make it. I look forward to working with him.??? ?? ?? ?? ????