The French Tennis Federation provisionally suspended Garcia and Mladenovic in August before clearing them to return last month.
The French Tennis Federation provisionally suspended Garcia and Mladenovic, the French number one and two respectively, in August before clearing them to return last month.
Mladenovic was accused of publicly criticising the federation after her and Garcia's defeat in the Olympic doubles.
She said in a tweet the federation failed to tell the players about tournament rules whereby they had to wear the same colours on court, forcing Garcia into a last-minute change of kit borrowed from her teammate.
The federation lifted the ban after the duo apologised, although it extended the suspension of male teammate Benoit Paire.
Garcia and Mladenovic will spearhead France's bid for a first Fed Cup title since 2003 on November 12-13 in Strasbourg.
They will be joined by Alize Cornet and Pauline Parmentier but face a strong Czech team led by two-time Wimbledon champion Petra Kvitova and sixth-ranked Karolina Pliskova.
The Czechs are chasing a fifth title in six years, but Mauresmo, a key player the last time France won the Fed Cup, is confident her underdogs can upset the odds.
"Of course the Czech Republic is favourite. But it's a sport. We are talking about sport. And this is what I said to the girls," said Mauresmo, former coach of Andy Murray.
"The ranking reflects 52 weeks, a whole season. What we need is just two days. So many things can happen over five matches.
"We were talking about their potential. Well, these girls are able to have very high-level moments in the season. They can rise to the occasion and they can beat extremely good players."