France

Paternity testing is regulated by the state and only allowed in certain cases:

Without a court order the express consent of the person must be obtained in writing before the carrying out of the examination, after the person has been duly informed of its nature and its purpose.

With a court order (if consent could not be obtained)

This is partially due to the official desire to "preserve the peace" within French families, with the French government citing psychologists who state that fatherhood is determined by society, rather than biology. French men often circumvent these laws by sending samples of DNA to foreign laboratories, but risk prosecution if caught. The maximum penalty for carrying out secret paternity testing is one year in prison and a €15,000 fine.

I got this from Wikipedia so I don't know if this is 100% true but if anybody is from France I'd like them to chime is as well because I find this pretty unbelievable.