The premise is asymmetrical. One could just as easily ask "Which regular medicine has been adopted as a folk remedy?", to which the answer of course is largely no. There is also a (purely pedantic) argument to be made that folk remedies are more 'regular', though assuming the question here is "Are folk remedies widely prescribed in their original forms by typical modern-day MDs?", the answer, again, is largely no.Now, to the question "Which folk medicines have a fairly robust (or at least promising) clinical basis?", there are certainly some: ginger[0], turmeric[1], honey[2], psilocybin[3], and of course capsaicin and peppermint. Not to mention sunshine, exercise, and meditation, all of which have traditional origins.
Taking a step back though, historically, pharmaceutical drugs have often been derived from natural remedies with bases in folk remedies. The pipeline from traditional medicine -> scientific study -> molecular isolation -> synthesis and mechanized production is pretty well-trodden. Aspirin comes from willow bark, morphine comes from opium, quinine (malaria treatment) comes from cinchona bark, paclitaxel (cancer treatment) comes from yew bark.
Homeopathy is BS though, no argument there. GP really shouldn't put it in the same bucket as folk medicine (it's not even particularly old).
[0] https://pmc.ncbi.nlm.nih.gov/articles/PMC9654013/
[1] https://pubmed.ncbi.nlm.nih.gov/36804260/
[2] https://pubmed.ncbi.nlm.nih.gov/37447382/
[3] https://pubmed.ncbi.nlm.nih.gov/35225143/