Miraculous: Tales of Ladybug & Cat Noir has a stellar cast of heroes who were uniquely chosen to wield the powers of the Miraculous. Each hero has their own abilities, similar to the Pokémon franchise, in which Pokémon are divided based on different elemental properties associated with both their "types" and their moves.
It would be interesting to see a Miraculous Ladybug/Pokémon crossover, however unlikely it is to happen. If Marinette, Adrien, Chloé, Alya and Nino ever took time out of their hectic world-saving schedules to take up Pokémon training, it would make sense for each of them to select an ideal team based on similarities between themselves and their Pokémon. Here are the Pokémon types each Miraculous hero would train.
Marinette/Ladybug - Bug Types
With "bug" in her name, it would be preposterous not to assume Ladybug would be a Bug type trainer. Her lineup could include Butterfree, Volbeat, Ledyba and Ledian. Presumably, her parter Pokémon would be Ledyba. Bug type Pokémon are known for their uniqueness, but they also represent the beauty of nature. Since Marinette is naturally beautiful, that metaphor feels appropriate.
Most Bug type Pokémon grow quickly and evolve sooner than other types, which is fitting for Marinette, who was the fastest to learn the ropes when chosen by Master Fu to become Ladybug.
Adrien/Cat Noir - Normal/Dark Types
Cat Noir is the one exception for dual-type Pokémon, as the Cat Miraculous is said to be the most powerful, therefore deserving of two types. As the Miraculous of destruction, Adrien seems suited to Dark types.
The Dark type is represented from traits that are considered feral and untameable, specifically those born from adverse and intense complex social conditions. For Adrien's complicated home life and reputation as a high school celebrity, "adverse" and "complex" are the right words to use.
Normal types are capable of learning most other types of moves, which relates to the "powerful" theory. Many normal types are also cat-like, which fits Cat Noir's brand. His ideal partner Pokémon would be Meowth, as their personalities are identical. His lineup would be a mixture of Normal and Dark types, including: Meowth, Skitty, Umbreon and Purrloin.
Chloe/Queen Bee - Poison Types
Since Ladybug has claimed the "bug" title, the next sensible option for Miraculous' Queen Bee would be Poison-type Pokémon. Queen Bee's special power is "Venom," which immobilizes her target. Poison-type Pokémon have a natural toxic quality, and some directly represent real-world species known for their venom, such as snakes. Venomous animals are often deadly when threatened; Chloé's feisty, hotheaded nature fits the "deadly" description, as her enemies (and even her classmates) do not want to mess with her.
Chloé's team could include the likes of Beedrill, Venonat, Seviper and Roselia. Beedrill would presumably be her partner Pokémon based on compatibility and likeness. Plus, both of them have "bee" in their names, which is a pretty good indication of solidarity.
Alya/Rena Rouge - Fire Types
In French, "Rouge" translates to "red." Fire is red, ergo, Rena Rouge would be a Fire-type Pokémon trainer, but not just for namesake. Rena Rouge is the definition of fiery: fiery hair, personality and spirit. Fire-type Pokémon can be a volatile handful, but Rena has the patience and persistence to train a flaming hot team.
Fire is notable for being one of the three Starter type Pokémon, forming a perfectly triangular relationship with Grass and Water. Additionally, Rena and Carapace, based on their romantic relationship in Miraculous, are a perfect type matchup.
Rena Rouge would have Fennekin as her loyal partner, especially as both belong to the "fox" species. Her remaining team would theoretically consist of Vulpix, Flareon and Growlithe, all of which are formidable Pokémon that are known to be difficult to train, but endlessly powerful.
Nino/Carapace - Grass Types
Grass-type Pokémon are among the gentlest types, perfectly compatible with Nino's protective and caring personality as Carapace. These Pokémon take many forms -- some are based on real-world plants, while others are simply animals with plant life attached to them. Turtles are omnivores and lovers of grasslands, which makes Carapace a prime candidate for a Grass-type trainer.
Turtwig would most likely be Nino's partner Pokémon based on the lookalike theme, but also for its resemblance to a terrestrial turtle, which is largely characterized by a domed shell to protect from predators. Quite aptly, Carapace's special power in Miraculous is "protective shell," seemingly making them the perfect Pokémon team.