In the Microsoft digital store, the product page of the game Far Cry 6 states that the title will be available May 26, 2021. Ubisoft has not yet officially confirmed this date.

There is no additional information on the release date on the page in the Microsoft Store is revealed but you can pre-order the title there. The Microsoft store has often been a correct source for release dates that were unknown until then. 

Far Cry 6 will be located in "Yara, a tropical paradise frozen in time." The main character we will play with will be Dani Rojas, who must join a guerrilla and fight to free his nation from the dictator Anton Castillo, who along with his son Diego is trying to take power by blood. In addition, Yara should become the biggest Far Cry map ever, where we will find jungles, beaches, and the capital city "Esperanza", having a vast number of sites to visit.

Microsoft product page.

Far Cry 6 looks to be released on May 26 2021