Unfortunately, the Gilets Jaunes don't have much support from existing political parties or even from Unions.
Macron's Great Debate has started. Basically he's willing to speak to the mayors, even from small towns, to everyone, except the Gilets Jaunes.
A couple days ago PM Philippe said he thought the RIC was "stupid". It's actually the main demand from the Gilets Jaunes : a referendum by popular initiative.
Sorry for maybe broken english : they want a referendum or plebiscite decided by the people themselves (for example, if more than 500k persons sign for it online, the State has to run a ballot, and the decision of the people becomes a law)