I am in Los Angeles for the last 2 months under the visa waiver & would love to go for 4 days to Mexico & back to Los Angeles. MY departure is on the 6th sept from LA. I hold a french passport. Can I go and back without a problem? do I need a permit?
Well we can't tell from the information you've given us, as it's down to how many days you spend in the US.
The VWP gives you 90 days, and this includes time in Mexico and Canada (ie it doesn't reset if you hop the border).
So as long as September 6th is still within the 90 days, from the US's point of view, you're fine.
Then it comes down to Mexico - you don't need a visa to visit as a French citizen. You will likely still need documentation of your travel plans - flights, accommodation and so on, but yes, you can do this.
If however, Sep 6 puts you OVER the 90 days, you're going to want to re-evaluate your flight dates, as that would make you an overstayer in the US, regardless of your trip to Mexico.