After ERDF have connected a temporary supply to a site for a new build, at what stage would they consider the installation sufficiently complete to be signed off to make the connection permanent?

They'd want to see a Consuel inspection certificate of conformity. That means you (or your electrician) gets Consuel around to confirm your electrics conform to french normes that were in place at the time you received your planning permission. Consuel take around 2-3 weeks to come and then get your certificate (as long as it conforms OK).

For the inspection the fuseboard and all sockets, light switches, earth connection etc need to be in place. Don't have to have heaters, boiler, light fitting etc. installed. Don't have to even have to have taped the plasterboard joints...Probably have to show bathroom layout to check for accordance to normes.