Actually I believe Péage is the name of the tollbooth

You'd know better than me! I came to think (wrongly?) they were synonymous. The (blue) toll road signs sometimes said "Péage" in italics, I thought, even if you aren't by the entrance (or at a point where you commit to the tollroad), and I thought I remembered getting directions from folks where they referred to it like "par la Péage" -- maybe shorthand/slang? (for dumb foreigners!) French road signs don't otherwise seem like they're big on brevity! -- "Vous n'avez pas la priorité!" versus. "Yield!"

My favorite? "Pensez aux enfants!" -- "Think of the Children!" Quite touching.