If you changed 'speak' to 'speaks' both would be acceptable English. However you should probably use this construction. He speaks English well. He speaks fluent English. If you used the second sentence, 'He speaks fluent English', the listener would understand that the person is proably not a native English speaker.

He speaks good English. He speaks fluent English. I speak, he speaks. Both are correct. 'Fluent' would be used more often to describe a person who understands a language when he/she hears it and can speak it without great effort to find the correct words and grammar. However, 'good' could be used and be understood.