Swansea boss Michael Laudrup says it is likely he will bring in a goalkeeper in January as Michel Vorm needs knee surgery.
Manager Jose Mourinho believes Ashley Cole will earn a contract extension at Chelsea.
The 23-year-old was at the goalless draw with Everton as he tied up a move for a fee believed to be in the region of £2million on a four-year contract.
Mackay said: "We have signed Kevin Theophile-Catherine from Rennes today.
"He is a good defender, he is someone we have tracked over the last year in France. He is someone who has pace, is aggressive and has good experience in the French top division, so he is someone we feel will be a good addition to our squad."
The move takes Cardiff's summer spending through the £30million mark after the acquisitions of Gary Medel, Steven Caulker, Andreas Cornelius, John Brayford, Simon Moore and Maximiliano Amondarain.