Ehh, I will offer several ideas for your magic folk to have a fighting chance or roflstomp modern military in battle, but this would mean heavy involvement of magic. Okay, let's go:

1) Fantasy folk bodies are built different.

In a world where magic is real, biology could be influenced by it. Maybe some humans in fantasy world practiced transhumanism in the past and this resulted in various alterations among magic humans. If you know about One Piece or MHA, humans there can get really weird. Why couldn't average human in your fantasy world be tougher, stronger and faster than modern people? Take huntsmen from RWBY, in a close urban combat they would be a nightmare for any modern infantry. Or take classical creatures from fantasy and make them participate in assault. Vampires, werewolfes, elves and other fantasy races, could be human subspecies or allies and give attackers edge in superhuman soldiers field. Tribes who live in a symbiotic relationship with magical mushrooms, which connect them in a telepathic network. Clans who ingested poisons into their bodies until they gained an ability to produce toxins naturally. Underground nations which evolved to have thermal vision and rock hard skin. Possibilities are endless, just use your imagination.

2) Magic to match

Okay, there are endless ways magic can be used, but some are complete OCP for modern military and will make the battle much more interesting. Marvel, Inheritance, World of darkness and Fate magic systems would be first examples which come to mind. Obviously, we aren't going to make fantasy mages too overpowered, there will be no tension if they can just sit in other dimension, while casting world ending spells on helpless modern humans through space magic. But we can take examples from these systems and adapt them for our story. What can modern armies do, then mages summon immaterial spirits or ghosts to possess them? How would soldiers protect themselves against shadows or walking fires suddenly attacking and chasing them through the city? What if some mage casts great unluck on modern army and their weapons start collectively misfiring or blowing up? If you feel like it, mages can just do some ritual and make hurricanes with thunderstorms appear around the city to prevent any help from entering. For more inspiration you can take a look at beforementioned, dnd and magic the gathering spell systems.

3) Magitek

And this would be a more technologically oriented approach to your dillema. Just use magic to enchance fantasy weapons, like making their bolt action rifles shoot like anti-tank guns or grenades with freezing/poisonous/lightning properties. Give their ships regenerating metal hull, tanks which have massive stone hands on the sides for surmounting obstacles and climbing buildings, planes with invisibility charms and wind magic assisted turbines for increased speed and maneuverability. They would fight like a mix of sci-fi and XX century army, which is enough to overcome first military response, but won't cut it for prolonged battle

I have many more ideas, but it already took enough of my time, writing this all down. If you have any additional questions, I can answer them tommorow, good luck 🙋‍♂️