Great question that I hope someone has an answer for. I distinctly heard a "d" sound between "vais" and "Paris." I misunderstood it the same way...

It's still Present tense in both languages. It is often used to refer to something that hasn't happened yet. This sentence is a perfect example of that. It does not rule out that you could simply say it a different way: J'irai à Paris demain = I shall go to Paris tomorrow. But that is a different sentence for learning purposes.