Você pode tentar assim.
SELECT client.id, client.name, GROUP_CONCAT(module.name) AS modules
FROM client
LEFT JOIN client_module ON client_module.client_id = client.id
LEFT JOIN module ON module.id = client_module.module_id
group by client.id Having Find_In_Set('module1',modules)>0 or Find_In_Set('module2',modules)>0
Demonstração do SQL Fiddle
