There are no credible free mechanic schools online. There are a number of courses and schools online that offer good rates for their courses and may even offer low monthly payments, like Penn Foster and Stratford Career Institute.
Learning to become a mechanic is a very hands-on and time-inclusive activity. The courses available online offer a lot of detailed and time-intensive information, so offering it for free is not something that the schools are able to do. It may be possible for someone working for a mechanic or automotive location to get the fees for the school reimbursed by his employer or be sent to school free through a program the business offers. .