If you franchise tag a player for $8 million, it costs $4 million (half) in current funds. I'm pretty sure the game actually tells you that when you attempt to place the franchise tag on a player. It's a dummy-proof "OK" popup to make sure you're well aware of that fact.
So all you have to do is go, "Do I have $4 million in current funds?". If yes, keep going. If no, don't continue with the process of franchise tagging that player because simple math says that doing so will put you in the negative.
I realize he was surprised that he couldn't sign any more players after going negative, but I mean...you've gotta imagine there's some kind of penalty to not having any more money.
Otherwise, what's the point of having a salary cap and guaranteed bonus money if you can essentially just pay all your players with Monopoly money that doesn't exist?