I am a French student at a University in Beijing, and want a job in Beijing after graduation. Do I need a new visa if getting a job offer?

International students in China are student visa holders, either with X visa or with F visa. According the governmental regulations, you have to leave China first and apply for a working visa in your own country or somewhere else like Hong Kong.

Where the foreigners can apply for a working visa within china?

If you are already in China, and you wanna renew your working visa or apply for a Z visa, the local public security authority is the place to apply for new visa. You can check out the local authority where you currently live to get detailed information.