Back-rower Conan, who suffered a foot problem against Italy a month ago, was the only member of Andy Farrell's 33-man squad to sit out training on Tuesday morning.
Hooker Sheehan took part in the session at the team's training base in Tours but will not be rushed back into action following the foot injury he sustained against England on August 19.
Prop Kilcoyne is returning to fitness following a hamstring issue.
Ireland forwards coach Paul O'Connell said: "Everyone's going well, there are a few guys still finishing their rehab and they won't be involved at the weekend.
"But by and large we're close to a full bill of health.
"Dan and Jack Conan (will not be involved). David Kilcoyne as well is struggling a little bit but should be OK next week."
Ireland begin the competition at the top of the world rankings and among the favourites to go the distance.
O'Connell is preparing for his first World Cup as a coach but has vast experience of the tournament having travelled to the 2003, 2007, 2011 and 2015 editions as a player.
The 43-year-old believes Ireland's squad are far better prepared than the last World Cup in France - a forgettable pool stage exit 16 years ago - and do not need to "reinvent the wheel".
Asked about the wisdom gained during his playing days, he said: "One of my experiences would have been in 2007 being over-trained a little bit and probably got the hotel wrong, got the food wrong a little bit and fuelling is such a big part of preparation.
"Your temptation as a player is to train as hard as you can but you need to leave something in the tank a little bit as well. And your temptation as a coach is the same, I would say.
"The other thing is sometimes you feel like you come to a World Cup and you need to reinvent the wheel a little bit.
"We want to evolve and get better for sure but it's not about reinventing anything and those are my two lessons.
"I think Andy, even though he wasn't involved with Ireland, would have had similar experiences and would be trying to put a similar strategy in place."
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