I had a similar situation in Paris with an iPhone. The Police were so helpful, knew exactly what to do, and were also very excited, but ultimately the Find My location wasn’t granular enough to find the phone. In an urban environment like Paris with big apartment buildings directly adjacent to each other, I think Find My is difficult. I’d have to be lucky and catch the phone during transit from one place to another, I think.
Edit: being able to use my iPad with Find My was an amazing experience, it’s almost worth having one just for that situation, where I didn’t have to bumble around with 2FA and logging in from my laptop, which isn’t Apple. I could also erase my stolen phone remotely, which gave me so much peace of mind.
"but ultimately the Find My location wasn’t granular enough to find the phone"
Depends on the generation, the new ones with ultra wideband (UWB) are really awesome, you can locate the item to tens of centimeters. I think you already have to be in a certain range for UWB to kick in. So might not really help if you could not identify the apartment otherwise.
The only real "problem" with UWB is the range. It might work better in North American homes (with hollow drywall walls), but in my Spanish home with brick interior walls, UWB doesn't even work one room over. It'll say "nearby", but completely lack any sort of direction information unless in the same room. I'd suspect in a situation like the OP was in in Paris, it would be very difficult to distinguish and exact location using UWB unless you got really lucky (like the phone was being stored directly next to an exterior door or something).
There should be an app people can download and you share the location data of your lost device. Multiple devices can all home in on it increasing resolution of the location via triangulation.
Edit: being able to use my iPad with Find My was an amazing experience, it’s almost worth having one just for that situation, where I didn’t have to bumble around with 2FA and logging in from my laptop, which isn’t Apple. I could also erase my stolen phone remotely, which gave me so much peace of mind.