The Belgian striker, Marseille's leading scorer, struck five minutes into the second half, applying a first-time finish to Benjamin Mendy's low ball into the box from the left.
That broke the resistance of their amateur opponents, who fought gamely throughout a quarter-final tie played at the Stade Michel-d'Ornano, home of Caen, Normandy's only top-flight representatives.
Granville, from a small town on the Channel coast, were forced to move the tie 100 kilometres away to Caen because their ground was deemed unsuitable for a tie that attracted a crowd of 20,000.
They rarely looked like scoring, but they made life difficult for their opponents, who saw Florian Thauvin come close twice in the first half.
Batshuayi was denied by an excellent Jeremy Aymes save just before he got the goal, and Marseille held on to set up a last-four tie in April away to Ligue 2 strugglers Sochaux, who eliminated Nantes 3-2 after extra time on Wednesday.
Marseille, who have not won the French Cup since 1989, remain on course for a showdown with their great rivals Paris Saint-Germain in the final, with the holders going to Lorient in the last four.
PSG won 3-1 at Saint-Etienne on Wednesday thanks to goals by Edinson Cavani, Marquinhos and Lucas as they got back to winning ways after suffering their first domestic defeat in almost a year at Lyon last weekend.
Lorient, winners of the Cup in 2002, secured their passage into the semi-finals by beating Gazelec Ajaccio 3-0 on Wednesday.