Farrell omits Carbery from Ireland's Six Nations squad
Ireland captain Sexton has been named despite recovering from a cheekbone injury, with Ross Byrne and Carbery's Munster teammate Jack Crowley named as his understudies.
Crowley impressed when he started last November's Test against Australia after Sexton had to withdraw at the last minute - and Byrne came on to seal the 13-10 victory.
That rounded off a year which saw Ireland rise to number one on the back of a sequence of strong results with the highlight a historic Test series win in New Zealand.
Sexton is expected to be fit to lead the world-ranked number-one side away to Wales on February 4.
Farrell, though, held out some hope for Carbery to regain his place over the duration of a tournament that is the last major test for European teams before the Rugby World Cup in France later this year.
Farrell will be seeking to lead the Irish to at least their first appearance in a semi-final of the global showpiece.
"While there are a few players carrying knocks and others that have missed out on selection for the start of the tournament, they will have the opportunity to push their case playing for their provinces in the URC over the coming weeks," said Farrell in an Irish Rugby Football Union statement.
"No doubt we will need to call upon the wider group as the tournament progresses."
Pivotal prop Tadhg Furlong has also been named despite carrying a calf injury but centre Robbie Henshaw misses out due to a wrist injury.
Veterans Keith Earls, capped 98 times, and Conor Murray, who has a century of appearances, are called up by Farrell even though they were both dropped for Munster's Champions Cup clash with Northampton last weekend.
Wing James Lowe, who recently returned to New Zealand for personal reasons, is also included.
The only uncapped player in the 37-man squad is centre Jamie Osborne.
The Irish follow up a week after playing the Welsh by hosting last year's Grand Slam-winning side France.
The Irish have lost to the French in their previous two meetings but will be bidding to record a record 13th successive home win over Fabien Galthie's side.
Squad:
Backs: Bundee Aki (Connacht), Ross Byrne (Leinster), Craig Casey (Munster), Jack Crowley (Munster), Keith Earls (Munster), Jamison Gibson-Park (Leinster), Mack Hansen (Connacht), Hugo Keenan (Leinster), Jordan Larmour (Leinster), James Lowe (Leinster), Stuart McCloskey (Ulster), Conor Murray (Munster), Jimmy O'Brien (Leinster), Jamie Osborne (Leinster), Garry Ringrose (Leinster), Johnny Sexton (Leinster, capt), Jacob Stockdale (Ulster)
Forwards: Ryan Baird (Leinster), Finlay Bealham (Connacht), Tadhg Beirne (Munster), Jack Conan (Leinster), Gavin Coombes (Munster), Caelan Doris (Leinster), Tadhg Furlong (Leinster), Cian Healy (Leinster), Iain Henderson (Ulster), Rob Herring (Ulster), Ronan Kelleher (Leinster), Dave Kilcoyne (Munster), Joe McCarthy (Leinster), Peter O'Mahony (Munster), Tom O'Toole (Ulster), Andrew Porter (Leinster), Cian Prendergast (Connacht), James Ryan (Leinster), Dan Sheehan (Leinster), Josh van der Flier (Leinster)
Coach: Andy Farrell (ENG)
