Under a J1 visa, you have a 30 day grace period to exit the country starting from the end of the program the J1 visa was for. The expiry of the visa is not relevant, and if the program you applied for has not ended you can continue in the country.
Assuming that it is the program that ends on February 28th, you have 30 days to exit the country, and cannot re-enter under the J1 visa. In any case you cannot re-enter on an expired visa. However assuming that you are a French citizen, you should be able to re-enter the US under the Visa Waiver Program at the end of your time in Mexico. You might be asked some extra questions because you entered so soon after the end of your J1, but as long as you can demonstrate that you intend to leave the US, especially if you are only transiting through, you should be fine. I would make sure you have your plane tickets out of the US with you, and ideally some other evidence that you live outside the US. This assumes that you have spent a substantial time in Mexico, not just exited and re-entered, and it also assumes you will be staying in the US only a short time.
If you want to return to the US for some other purpose you will need another visa.