A guy goes to the bathroom, leaves the seat up and doesn't flush the toilet.
Then a girl goes to the bathroom, and without really looking or thinking, sits down on the open toilet seat.
Since the seat was left up, she falls in. Her labia "dip" into the dirty toilet water, and as they do, she exclaims, "Au Jus serious!?!"
Thus: the french dip
The Situation had just peed in the toilet and he left the seat up. Snooki was drunk and she went into the bathroom for a pee. She fell into the toilet, and she french dipped into the dirty toilet water.