Gilchrist was given his marching orders for a dangerous tackle on Anthony Jelonch during a 32-21 victory for the defending champions at the Stade de France last month.
The 32-year-old could have faced a six-week suspension, but an independent judicial committee ruled that he must miss out three matches.
Gilchrist will sit out a clash with leaders Ireland at Murrayfield on Sunday and Scotland's final game of the tournament at home to Italy six days later.
The forward will be cleared to play for Edinburgh against Connacht on March 25 once he has completed a tackle course.
Scotland is second in the table, five points behind Ireland after Les Bleus consigned them to a first defeat of the tournament.