The novel is essentially the story of Gervaise Macquart, who was featured briefly in the first novel in the series, La Fortune des Rougon, running away to Paris with her shiftless lover Lantier to work as a washerwoman in a hot, busy laundry in one of the seedier areas of the city. L'Assommoir begins with Gervaise and her two young sons being abandoned by Lantier, who takes off for parts unknown; she later takes up with Coupeau, a teetotal roofing engineer, and they are married in one of the most famous set-pieces of Zola's fiction; the account of the wedding party's chaotic trip to the Louvre is perhaps the novelist's most famous passage. Through a combination of happy circumstances Gervaise is able to raise enough money to open her own laundry, and the couple's happiness appears to be complete with the birth of a daughter, Anna, nicknamed Nana (the protagonist of Zola's later novel of the same title).
The second half of the novel deals with the downward trajectory of Gervaise's life from this happy high point. Coupeau is injured in a fall from the roof of a new hospital he is working on, and during his lengthy and painful convalescence he takes to drink. Only a few chapters pass before Coupeau is a vindictive alcoholic, with no intention of trying to find more work; Gervaise struggles to keep her home together, but her excessive pride leads her to a number of embarrassing failures and before long everything is going downhill. The home is further disrupted by the return of Lantier, warmly welcomed by Coupeau—by this point losing interest in both Gervaise and life itself, and becoming seriously ill—and the ensuing chaos and financial strain is too much for Gervaise, who loses her laundry-shop and is sucked into debt. She decides to join Coupeau in the drinking and soon slides into heavy alcoholism too, prompting Nana—already suffering from the chaotic life at home and getting into trouble on a daily basis—to run away from her parents' home and become a streetwalker. The novel continues in this unhappy vein until Gervaise dies.

Question: Who becomes an alcoholic besides Coupeau?
Answer: Gervaise.
Alternative answer: Gervaise.