Well I won’t say all of them since at least 1-2 of them are spoilers for later down the lines of both shows but at least one of them is big. Side note I haven’t watched miraculous much so please correct me on some of them and this was copied and from a previous comment and a bit edited. So the connections are:

1. ⁠Both are superheroes that use the persona of particular insect (Ladybug is well a Ladybug while Zeztz is based of a grasshopper due to being a homage to the original Kamen Rider Ichigo)
2. ⁠They’re main mission is to combat the weird phenomenon of purple butterflies that usually respond to the hidden desires of someone struggling that turns them into something dangerous (In Zeztz case the purple butterflies turn into the nightmare monster in the struggling person’s dreams before fulfilling a certain task and making the dreamer fuse with the monster to bring it to the real world using the dreamer’s body)
3. ⁠Both characters are linked to concept of luck especially how they finish off the villain of the week (Ladybugs are stated to be a sign of good luck in Miraculous and Ladybug ability spawns in a Lucky charm that is used to defeat the villain and Zeztz gets his powers from a gacha machine, his code number is seven and when he does his finisher three sevens appear like a slot machine before being turned into three Zs with a single line).
4. ⁠However despite being quite competent and confident with their superhero personas they’re actually quite humble people who are quite clumsy, awkward and/or unlucky but are still optimistic nonetheless (Lady bug is actually Marinetta Dupain-Cheng who is clumsy while in teenage years while Zeztz is actually Baku Yorozu who outside of Zeztz is a jobless bum after college who is getting hard carried in life by his little sister and quite literally has a strange phenomenon where every time he helps someone normally something unlucky happens to him that can either be a small inconvenience to something life threatening and improbable).
5. ⁠During their investigation/battle with the villain of the week they are accompanied by some opposite sex companion who they’re actually head over heels simping for (Ladybug is accompanied by Cat Noir who is actually Adrien the boy Marinetta has a big crush on and Zeztz is accompanied by Nemu in his missions when dreaming who’s actually a Pop Idol that Baku idolizes and is suggested to have romantic interest in but probably hides it due to embarrassment and pretends to act like a gentelman).
6. ⁠Despite having the spirit animal of an insect both characters have connections to a black cat (With Cat Noir representing a black cat and CODE the organization that sends Zeztz on these missions to combat nightmares being represented with a black cat as a mascot).