The roll-out of fines follows tests in cities such as Rennes and Marseilles, the BBC reported.
The 200-euro ($23) fixed fine will reduce to 150 euros if paid within 15 days.
Castex made the announcement on Saturday while on a trip to Nice, which has seen weeks of drugs-related violence, including in its Moulins district, where shots were fired in broad daylight outside a supermarket this week.
He said the system would come in at the start of the beginning of the school year after the summer break.
A part of Castex's plans to strengthen security, the Prime Minister said he wanted to "put an end to the violence of everyday life" .
He said the drugs measure would simplify police procedures by "inflicting punishment without delay".
France, one of the leading consumers of cannabis in Europe, already have laws that allow for up to a year in prison and fines of up to 3,750 euros for the use of illicit drugs, without specifically distinguishing drug types, the BBC report said.
But the laws, dating back to 1970, seldom lead to prison sentences, with magistrates preferring alternative punishments, often warnings.
Although there is the reduction for early fine payment in the new system, if an offender fails to pay up in time it increases to 450 euros.