Forever a WIP - please don't be shy about suggesting additions!
This list began using the video essay "Jacques Demy A to Z" by James Quandt (included on the Criterion Demy box set) and it's title as a starting point for tracing connections between Demy's a) influences, b) contemporaries and c) influencees.
As is, this is essentially grouped into those three categories. Each section is internally organized by relevance.
The periods of influences, contemporaries and influencees roughly correspond to (-1960), (1960-1970) [because after this period Demy's films received much less contemporaneous attention or clout] and (1970-present). These distinctions are loose.
If an entry only lists the director's name that means it's from the video essay and I can't fully explain the connection.