Western Europe during the Medieval Period used the Julian Calendar introduced by the Romans, because, well, the Roman Empire kind of created the idea of Europe too a degree. The White Western European cultures left behind in the area of former Western Rome saw the Roman Empire as a defining shared trait; well before whiteness and European-ness were formalised in the 17th-19th century.

The main difference between our time schedules is that the Julian Calendar does not match up to the modern Gregorian Calendar; the days are around ten apart. For example January 2nd of 1603 in the Julian Calendar was the 12th January to those who had started using the new 16th century Julian Calendar (Catholic countries; it was after all invented by researchers working for the Pope). Additionally, and one of the main differences that relates to its different timing, is that the new year officially starts on Lady Day, 25th March, although countries with the Julian Calendar could still celebrate a December new year as they did in 16 and 17th century England (two new years is just bizarre it must be said).

If you want to calculate what a Julian date was before the Gregorian adoption in a county; you can use this resource:

https://stevemorse.org/jcal/julian.html

And this once can compare them side-by-side starting from when the Gregorian was officially adopted:

http://5ko.free.fr/en/jul.php?y=1582

The day Sunday was introduced into the Roman Calendar during the 1st and 2nd centuries with influence from Egypt. In the 2nd century this was also the time that the Lord's Day Sunday and Easter Sunday began to be celebrated and emphasised by early Christians, partially to differentiate themselves from Jews because the Roman emperors began to prefer Christians and they wanted to separate themselves from the unpopular Jews. This coincided with a conspicuous rise in anti-semitic literature from the early Christians (see From "Sabbath to Sunday: A Historical Investigation of the Rise of Sunday Observance in Early Christianity" by Samuele Bacchiocchi, 1977). Sunday was later supported by the Christian Emperor Constantine in 321.

The English names for the days are derived from the Roman seven day week, where they were referred to by gods associated with the planets or referred to as the days of those planets. Monday is just moon-day because there were no clear enough counterparts, while Tuesday and Thursday for example were named after Germanic counterparts to the Roman gods; Tyr instead of Mars, Thor instead of Jupiter. The middle English name for Monday is monedæi and mōndæg in Old English, if you want to know, but that's more to do with English linguistic change than any conscious change of etymology (it's obviously just the same word altered).