Wales flanker Dafydd Jones has been ruled out of all of the rest of the Six Nations because of a pelvic injury. A groin strain meant the 25-year-old was a late withdrawal from the side that beat Italy, and he has now been told to rest for six weeks.
But winger Hal Luscombe is hopeful of being fit after hurting a hamstring.
Ryan Jones (collarbone) should also be fine, whilst prop Duncan Jones will be released for regional duty this weekend after recovering from a broken thumb.
The loose-head faces a battle to oust John Yapp as Gethin Jenkins' back-up, though, with Yapp having impressed in cameo appearances from the bench against England and Italy.
Said Wales team physiotherapist Mark Davies: "Dafydd has a pelvic condition known as Osteitis Pubis which is currently preventing him from running.
 | Martyn Williams' knee stood up well to the physical encounter with Italy and he has had little reaction |
"Ryan Jones is progressing well with the A/C joint injury to his shoulder and he is taking part in fitness and conditioning training this week.
"He will be reviewed and, subject to a fitness test, should be in contention for selection to face France.
"Duncan Jones is set to be officially released to play for his region tomorrow (Tuesday) after recovering from a broken thumb.
"Colin Charvis is not likely to return from his foot injury in time to travel to France, but should be able to undertake light training next week.
"Sonny Parker's neck injury remains an issue and he is not currently involved in any contact training.
"He will be continually monitored and will be tested again next week to verify his fitness.
"Hal Luscombe left the field on Saturday with a hamstring injury, but he is responding to treatment this week and will hopefully progress to making himself available.
"Martyn Williams' knee stood up well to the physical encounter with Italy and he has had little reaction which bodes well for next week."
Lock Luke Charteris, who has been sidelined with a rib injury, is ready to return to action and could play for the Dragons in the Celtic League on Friday.
Team-mates Ian Gough and Gareth Cooper are nursing shoulder injuries and are unlikely to play against Ulster.