The 22-year-old Francis is in contention for Saturday's round three clash with Racing Metro at the Stade Yves du Manoir after recovering from a leg injury which has kept him out since he moved to Murrayfield last month from Waikato Chiefs in New Zealand.
Rennie suffered a dislocated shoulder against the All Blacks in Scotland's opening autumn Test on November 11.
Edinburgh head coach Michael Bradley said: "It's obviously disappointing for Ross to be ruled out for these next two rounds.
"However, it's a fantastic opportunity for a new member of our squad to push for a place in the best club rugby competition in the world."
Gilbert has released a new line of rugby cleats. The Gilbert Virtuo 8S is part of the exciting new product. Check it out.
The Barbarians are one of the top invitational rugby sides with a long history and classic rugby jersey.
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Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
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The Lions are ready to get their Australia tour underway. They arrive in Perth on Monday.
The New Zealand All Blacks training jersey for 2013/14. Get in the Gear!
The USA Rugby Pro Alternate rugby jersey is perfect for any fan of the Eagles. Get yours to wear during the summer Test matches.
The NEW All Blacks 2013/14 jersey has arrived at World Rugby Shop. Dare to wear the colors of the All Blacks.