The issues add to Galthie’s selection problems. Leo Barre has yet to join the squad as he recovers from the injury that ruled him out of the tour warm-up match with England.
“There were some problems during training but we have yet to hear back from the medical staff,” said assistant coach Laurent Sempere.
To make up for the absences of Villiere, Tiberghien and Spring, Galthie slotted in Theo Attissogbe at fullback and Emilien Gailleton and Alivereti Duguivalu on the wings.
The squad will be strengthened for the second and third tests – in Wellington on July 12 and Hamilton a week later – by five members of the two Top 14 finalists, Toulouse and Bordeaux-Begles.
They will be named when the results of fitness tests performed after Saturday’s final are known.
Toulouse retained their title after beating Champions Cup winners Bordeaux-Begles 39-33.
For live commentary of this weekend’s All Blacks v France test, go to GOLD SPORT or iHeartRadio.