Flood, who came off the bench in the defeat by Wales at Twickenham two weeks ago, has been released from the England squad to play for Leicester in Saturday's LV= Cup semi-final against Bath.
Owen Farrell is expected to be retained at fly-half for England's trip to Paris following his impressive performance against Wales, with Hodgson set to return from a finger injury on the bench.
The Saracens fly-half had started England's opening victories over Scotland and Italy before suffering the training-ground injury, which prompted Farrell's successful switch from inside centre.
England coach Stuart Lancaster will be forced to make one further change to his 22-man match-day squad after lock Courtney Lawes was ruled out of the championship with a shin problem.
Tom Palmer would be the likely choice for a place on the bench after being dropped for the Wales game as England looked to tighten up their lineout.
Lancaster names his squad on Friday.
Leicester number eight Thomas Waldrom, Bath hooker Lee Mears and Northampton pair Paul Doran-Jones and Calum Clark have also been released for the LV= Cup duty this weekend. Northampton play the Scarlets on Sunday.
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