The World Cup will include female referees for the first time at a major men's international tournament, with Michael Oliver and Anthony Taylor also selected to adjudicate.
Three female referees and three assistant referees who have already been paving the way for female officials in the men's game are included in the list.
In recent years, Frappart has become the first female to referee a European match and has also taken charge of games in France.
The first woman to referee a match at the Africa Cup on Nations was from Rwanda.
The first woman referee to take charge of a match in the Asian confederation was from Japan.
The assistant referees are Neuza Back from Brazil, Kathryn Nesbitt from the USA and Karen Medina from Mexico.
The deployment of female referees at the men's junior and senior tournaments began several years ago, according to the chairman of the referees committee.
It is quality that counts for us and not gender. I hope that in the future the selection of elite women's match officials for important men's competitions will be seen as normal and not as sensational.
They deserve to be at the World Cup because they perform at a really high level, and that is the important factor for us.
The group of 36 referees include Oliver and Taylor, as well as Simon Bennett, Gary Beswick, Stuart Burt and Adam Nunn. A team of 24 VAR officials will also be present.
The selected match officials represent the highest level of refereeing in the world. We will do our best to be even better in a few months, partly because of the high standard of refereeing, and also because the World Cup was very successful.
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The Pandemic affected our activities in 2020 and at the beginning of 2021. We had enough time to give the candidates good preparation for the World Cup. We want to work even harder with those who have been appointed for the World Cup, so we are announcing these selections well in advance.
The message is clear: don't rest on your laurels, keep working hard and prepare yourselves very seriously for the World Cup.
The selected match officials will take part in several seminars this summer, reviewing and analyzing video clips of real match situations, and taking part in practical training sessions with players which will be filmed to give participants instant feedback from the instructors.