web server access redundancy

I have two internet sources. One our primary and the second is our fail over.
We have a web server behind our firewall that is linked to a public static IP from the primary internet provider- we are forwarding port 80 to web server. My question is if the primary internet goes down which we will then use our failover internet how will people from the outside be able to access our web server if the public DNS is pointing to the primary internet provider static public IP. Our second internet connection is also behind a firewall..