וַיְהִ֗י אַחֲרֵ֛י מ֥וֹת מֹשֶׁ֖ה עֶ֣בֶד יְהוָ֑ה וַיֹּ֤אמֶר יְהוָה֙ אֶל־יְהוֹשֻׁ֣עַ בִּן־נ֔וּן מְשָׁרֵ֥ת מֹשֶׁ֖ה לֵאמֹֽר׃
Après la mort de Moïse, serviteur de l’Éternel, Dieu parla ainsi à Josué, fils de Noun, qui avait servi Moïse:
Rashi
And after the death of Moshe. This is connected to the chapter of the Torah1The spirit of prophecy did not rest upon Yehoshua until the thirty day mourning period for Moshe was over. It was then that God began to speak to him and command him to begin the conquest of Eretz Yisroel. Yehoshua was in a state of sadness and the spirit of propecy does not rest upon a person who is sad. There are other Seforim in Tanach such as Ruth, Esther, Yonah that begin with the word וַיְהִי, and it was, that are not connected to any previous event. But here the beginning is definitely connected with the conclusion of Sefer Devorim where the death of Moshe is related. which concluded with the passing of Moshe;2Devorim 34:5,6,7,8. and this (Seifer Yehoshua) is connected to it.3Devorim 34:9.
Metzudat David
The Vov comes to add, and to connect, to what was completed in the Torah, with the story of Moshes death, and after this, Hashem said to Yehoshua etc.
Metzudat Zion
[Bin nun] is written with a "chirik" rather than [the more common] "segol", because they are small and connected words, [the bin and nun are connected], it is easier to read [the word Ben] with a "chirik" than a "segol".