"我不会说中文" is correct.
但有时得说“我不能说中文”。比如,我是一个中国人,要参见一个国际会议,我可能对别人说:“明天我要参见一个会议。那是个国际会议,我不能说中文。”It means that I will have to speak some language other than Chinese (Possibly because it's a rule. Possibly because most of people who will attend the meeting don't understand Chinese and there will be no interpreter)