The Gregorian calendar also fixed the first day of the year as January 1, which was already the first day used in Italy, Germany, and other places, but not universally (the British Empire, for example, began the year on March 25). This is why the months named after the Latin numbers 7, 8, 9, and 10 (September, October, November, December) are now the 9th, 10th, 11th, and 12th month, respectively.
I have removed this last line, because it is incorrect. The shift from March 1 to January 1 as the first day of the year was already made when the Julian Calendar was installed.