Japanese seems to use Western/Latin names for days of the week (e.g. Sunday = 日曜日 lit. sun weekday) which I assume isn't just a huge coincidence, so I wondered what they used beforehand, and whether there are any examples of calendars without seven-day weeks.
Japan adopted the Gregorian calendar only in 1873, as part of Meiji Era modernisation. Prior to this they used a Chinese calendar. However, names for the week days based on the 7 'planets' like in the West are much older, having been brought over with the Buddhist Calendar around 800, though until 1876 these were only really used for astrological purposes.
Sorry, that was possibly the worst example I could have chosen... Monday is 月曜日 (moon day, as French and English) but then Thursday is 木曜日 (tree day, with tree also being in the name of Jupiter, as French jeudi).