Warburton was due to undergo what Wales forwards coach McBryde described as a "rigorous fitness test" after missing the 24-3 victory over Italy because of a knee injury.
Wales' World Cup skipper has played in just one-and-a-half games of this season's Six Nations, with his knee problem following thigh muscle trouble that forced him off at half-time against opening opponents Ireland.
"Sam will be undergoing a rigorous fitness test, and we hope he comes through it and takes a full part in the remaining sessions this week," McBryde said.
"We will then have a better understanding of where he is at. He has stood up well in every fitness test he has done.
"Things are looking favourable, but we know we have a good player in Justin Tipuric, who acquitted himself well at the weekend. It is not quite panic stations."
McBryde reported a clean bill of health among the players after the Italy success left Wales one win away from sealing their second Six Nations crown and Grand Slam of coach Warren Gatland's four-year reign.
Warburton for Tipuric is likely to be the only change when Gatland announces his team on Thursday, assuming the inspirational Cardiff Blues flanker proves his fitness.
France will arrive in Cardiff on the back of a 24-22 home defeat against resurgent England, a result that ended their Six Nations title hopes.
But they have won five times and lost once on their previous Millennium Stadium visits in the Six Nations, which is a record the Wales camp will not overlook.
"France will rue missed chances and wrong options, but if they gel they will be a stern challenge," McBryde said.
"You cannot take anything for granted when you play France.
"For us, how you finish a championship is as important as how you start it. The expectation to deliver a strong performance will be high, and the players will be keen to give a good account of themselves."
McBryde also dismissed a contentious World Cup semi-final between the countries in Auckland last October as having any bearing on this week's eagerly-awaited rematch.
Wales lost 9-8 after outplaying France for an hour following Warburton's sending-off by Irish referee Alain Rolland for a dangerous tackle on Les Bleus wing Vincent Clerc.
"That is not a road we will be going down," McBryde said.
"We know what happened in the semi-final, and I suppose it will be built up as a rematch and revenge.
"Every match is different - the playing personnel will be different and so will the referee.
"It will be all on the day, and any thought of the World Cup should be dismissed. It's about the here and now, what is at stake and what could be achieved if we perform."
Wales started their Six Nations campaign with an exhilarating display in Dublin to defeat Ireland, while a 20-minute purple patch accounted for Scotland, but the latest two performances against England and Italy did not see them find top gear.
"The confidence is there, but we know we have under-performed in the last couple of games and need to step things up," McBryde said.
"We hope the pressure of playing France at home will bring out the best in the team. We finished 2008 at home to France, and that could be a help.
"No-one knows which France will turn up, as is the case historically. They are hard to analyse.
"They will want to prove they are not as bad as some in France make out, and they will want to finish on a high. It will be a test for us.
"The management group know what happened in 2008, and there is enough experience to ensure that we do not go overboard or change things too much.
"Warren told the players immediately after the game on Saturday that this was going to be a tough week and that, learning lessons from the past, we would not be taking our foot off the pedal.
"We cannot afford to step back. Training will be quite tough and competitive to ensure we finish strongly in the last game."