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 entire All Blacks apparel line has been updated for 2013/14. Check out the New Zealand All Blacks polo.
The Nike Tiempo is a solid rugby cleat and one of few styles still made from full-grain natural leather.
The Gilbert Blitz 8S rugby cleat is a great cleat at a great price of $69.99. Get a new pair of cleats today.
A cool looking all black rugby cleat with the high performance adidas is known for. Get in the Gear!
Wear the crest of the British and Irish Lions on your t-shirt. A great look for the summer.
The All Blacks Performance t-shirt is black with hints of blue from the training jersey. Very Cool.
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.