THEORY:
First of all we know that Shanghai special takes place between Season 2 and 3 events while New York Special takes place between Season 3 and 4 events. Next we know that Cash was connected with both the events and so definitely will have something to do with this “One night mission”. But something that’s more interesting is in both the specials there was mention of not only a new miraculous box and guardian but also the existence of Prodigious which was abandoned. 
We did see how Mei Shi, who appeared from the bracelet mentioning that it is not end of his mission, it was only the beginning thus foreshadowing the possibility of more of Lady Dragon’s adventure.
Then in New York Special, we saw a new guardian with another miraculous box who met Eagle and was trying to get the Miraculous back from her which was foreshadowing the existence of other miraculous box apart from the one that Ladybug has with her now. But something that was interesting how Eagle mentioned to create a new generation of heroes together to which the Monk agreed so this could be yet another foreshadowing the possibility of seeing new holders of other miraculous that’s in that box and may be we might see them in this so called “One night mission.” Though we don’t know where exactly it is going to take place but we can assume it might take place in Paris itself where all the heroes meet up for yet another fun adventure. Plus it would also give away the possibility of new Lady Dragon’s series which was hinted by Jeremy Zag.
What if Fei comes to visit Marinette in Paris and what if Jess too comes to meet Ladybug? We did see how she was there at the same spot where Cash made an appearance for the first time and may be we will get some more information to this, possibly a continuation to this part in Paris. We also know how much Cash is obsessed with power and money and his link with Nathalie too will turn out to be a big threat for both Ladybug and Cat Noir too leading them all forced to deal with him together in a new special mission. What if this time Cash comes to meet Nathalie or may be he got a hint of Hawkmoth been in Paris which leads him to come to Paris in search of him or follows Fei to get the Prodigious back from her?
BONUS:
Bonus to this discussion is this particular scene from Timetagger episode where we got a hint about a future villain. If you remember clearly Bunnyx had mentioned that how Ladybug will come across a villain named Ignoblia, the evil sister of Majestia in the future, so what if this was a foreshadowing of this particular special mission? We don’t know who this so called evil sister of Majestia would be but I strongly feel it could be Barbara Keynes, the Knightowl. May be we will get to see her akumatized as Ignoblia. Another possibility is that may be Majestia actually has a sister whom we have never seen and may be she might introduced in this mission.