As noted on the main page for this section, while the Martian sidereal year can be determined to higher precision, we only know (from this site) that a Martian tropical year is 686.97258 Earth days long, or 668.592018 Martian days long.
Because the orbit of Mars is strongly elliptical, this site proposes that the Martian calendar should reflect not only the average length of the tropical year, but also its periodic changes in length due to that effect. This is a complication that is not familiar from methods of timekeeping used upon Earth. A conventional calendar would simply give Mars three leap years out of every five, changing that to two leap years out of five once every 125 Martian years or so.
If we divided the Martian year into twelve months directly, with the goal of imitating the Earth calendar as closely as possible, what would it look like?
668.592 days in a year would probably mean that six years out of every ten, except for one year in every hundred, would be leap years, as has of course already been proposed.
Trying to make the pattern of the lengths of Martian months correspond to that of Earth months might lead to column B in the following table:
A B C A B C
January 31 57 56 July 31 57 56
February 28* 53* 55* August 31 57 56
March 31 57 56 September 30 54 55
April 30 54 55 October 31 57 56
May 31 57 56 November 30 54 55
June 30 54 56 December 31 57 56
but I think it is obvious that something like the arrangement in column C, which would make the lengths of the months more regular, if not something even more regular and symmetrical, would be preferred.