not a dead head flight but an empty leg
these flights at the start or end of a summer season are called
empty legs, not dead head as you describe.
dead head is a term for air crew non-operational travelling as pax sometimes
in jump seats.
duty travel is where airline staff or crew are travelling on duty and/or
positioning sectors in passenger seats.
empty legs were the pain of all tour operators and they always tried to sell one-ways as you describe but in the old days there were often regulations forbidding charter airlines and tour op's in selling these seats to nationals of the destination or origin.
rules are somewhat relaxed now to most places.
chances are yours maybe almost empty to DBV but you never know these days!