The received wisdom is that the grapheme ou in early 17th-century Middle French was already /u/, and that this /ou/ > /u/ became established through Middle French from the late twelfth to the thirteenth centuries. However this is somewhat questioned by certain scholars, who point to a retained diphthong /ou/.
During the 16th century, amongst the grammarians there was much debate about the acceptability of the ouistes, which were those who were merging etymological o /o ~ ɔ/ into ou /u/ in lexemes such as chose (vs chouse) et arroser (vs arrouser). Naturally the grammarians differed in opinion on this, with assertions of different regional divides, but in general agreeing that a pronunication with o (presumed /o ~ ɔ/) was the northern pronunciation. By 1618, French ambassador to the Scottish-English court Maupas mentioned:
Le son de cette voyelle est assez notoire. Depuis peu en ça on affecte une niaise & vicieuse prononciation en ce mot Chose, & dit-on Chouse: autres Cheuse, ce que ie n'approuve.
The debate continues through the early 17th century, though it seems the standard orthography is settled upon by the middle of that century, even if it masks variation in pronunciation.
A 2017 paper casts doubt however on the consensus that ou already represented /u/, citing several pieces of evidence. Vaugelas' 1647 Remarques sur la langue française consistently calls the grapheme ou a diphthongue. However, that may just be an issue of nomenclature.