The GMM is an annual rally held at different locations across the planet, now in its 15th year. Pro-cannabis rallies were held last weekend in several cities across France such as Marseille, Toulouse, Lyon, Bayonne and Poitiers.
Among the arguments for the legalisation of recreational marijuana use: less trafficking, better products and perhaps less crime.
Others say marajuana offers relief for the terminally ill.
Cannabis use has been illegal in France since 1970, punishable by one year in prison and a 3,750-euro fine. In practice, imprisonment is rare, although fines continue to be meted out.
Green Party member and Val de Marne Senator Esther Benbassa is calling for fresh legislation on what she sees as a "public health problem".
A bill proposing the state-controlled sale and use of cannabis was shot down in April, largely thanks to some people's moral objections, she said.