First of all, to be eligible to apply for admission for the BFM course, you should have passed class XII from Maharashtra state board or any other board with an aggregate of minimum 45%. It is not compulsory to have a commerce background to get admission in this course.As regards the procedure, first you apply on the mumbai university website. There you make your account and from their you can apply to various colleges and courses as per your choice. Thereafter, you have to physically go to the colleges where you want admission to submit the necessary documents like 10th and 12th marksheet, passing certificate, etc.
  Once your documents are submitted, you wait for the merit lists to come out. There is NO entrance required. Usually about 5-6 merit lists come out and if your name is there in any of those, you again have to go to college and confirm your admission.


Feel free to comment if you have any doubt
Good luck