The French were highly critical of an evaluation report which said South Africa should be chosen. The remaining members of the World Rugby Council disagreed with the report and voted overwhelmingly for France.
"In the feedback sessions I am sure we will be recommending to the World Rugby Council that the verdict of the evaluation committee become binding," said Jurie Roux, CEO of SA Rugby.
"World Rugby ran an exhaustive and transparent process for 15 months to identify the best host nation, only for the process to go entirely opaque for the past two weeks."
SA Rugby president Mark Alexander added: "We are bitterly disappointed at this decision and would like to apologise to the people and government of South Africa for raising their hopes."