France's Lucu a doubt for Six Nations opener
The injury comes after Lucu, 32, played the full 80 minutes of Bordeaux-Begles's French Top 14 win over Racing 92 on Saturday.
"If he works hard, it will be four weeks," Bru told AFP. "If not, it will be six."
France start the defence of their Six Nations title on February 5 against Ireland in Paris. Lucu had been expected to start on the bench as back-up to the returning Antoine Dupont.
Bordeaux-Begles play a Champions Cup pool stage match against Northampton on Sunday, in a re-run of last year's final.
Superstar Dupont has been sidelined from France duty since last March after suffering a serious knee injury against Ireland in the Six Nations.
Since returning for club Toulouse in late-November, the 29-year-old has scored three tries in five games including a stellar double against La Rochelle on December 28.