What grade is your child in? I would only be concerned if they are in high school.
I believe they will allow you to stay until the end of the year if your child has transportation. It is a process called COSA, which can be challenging to navigate, but in this situation should be an easy yes especially due to the language class.
If you can't make that work, they will figure out the grades. It would be easiest to switch at a natural transition time- the end of the semester, but they will figure it out regardless of what day your child starts.