The tense is present simple. Grammatically, the construction 'has ... to say" is similar to the patterns in "He has [some work] to finish" or "He has [some money] to spend" or "He has [nothing] to do". If you have something to say about a situation, this means that you have an opinion which you want to express. "Let's see what else he has to say here" means this: "I'm sure that Jack has something else to say about this situation. I think we should let him say it."

Normally "have to" means that you "must" or "need" do something. For ex., I have to go to my work (the meaning will be - I must go to work). But in your sentence "he has to say" - means exactly what the previous girl told you - That means "he has something in his mind to say and we should ask him, what is in his mind".