Cheyrou volleyed home Charles Kabore's cross at the far post in the 77th minute of the Ligue 1 game after the nine-times French champions dominated the second half.
Reims won six French titles, all between 1949 and 1962 and also reached the European Cup final twice in the early days of the competition.
But they have hit troubled times since relegation in 1979, at one point dropping into non-league football amid severe financial difficulties, and were in the third tier only three seasons ago.
Cheyrou's goal gave Marseille coach Elie Baup a winning league start after he stepped to replace Didier Deschamps who left after three seasons to take charge of France.
Marseille are aiming to improve on last season's 10th place, their worst finish in more than a decade.
- Charles Kabore