Atonio was sinbinned, and was somewhat lucky to escape being sent off, in France's 32-19 defeat after his tackle forced Herring off for a head injury assessment, from which he did not return.
The La Rochelle player's suspension will be cut to two matches provided he completes a Coaching Intervention Programme, known by many as ‘tackle school’. In that case he will return for France's final Six Nations showdown with Wales on March 18.
"The player admitted that he had committed an act of foul play worthy of a red card. Having reviewed all the evidence, the committee accepted the player's admission that the tackle on Ireland number two was foul play," the Judicial Committee said in a statement.
"His shoulder made contact with Ireland number two's neck/face as described in the Citing Commissioner's report and therefore reached the red card threshold.
"On that basis, the Committee applied World Rugby’s mandatory minimum mid-range entry point for foul play resulting in contact with the head."
Atonio will miss the matches against Scotland on February 26 and England on March 11.
