LOL!
I (still) run with my reliable '04(!) Garmin Quest-I...
Already in 2006 Garmin decided to discontinue their City Select map-sets and switch to City Navigator... not compatible with the Q-I... (right... you ought to buy a new kit every year...

)
So since 2008/09 I'm working with/on OSM maps...
Back then a seriously "scientific", lengthy, multi step ordeal to get those onto your PC and then onto the little navigation assistant...
You could only download & install each country individually, neither the plotting software (MapSource) nor the GPS unit were able to calculate/navigate across borders...
so you had to cut the routes right at the border crossing, switch the active map & start the next leg of the tour... and the same procedure backwards on your way home...
No comparison to these days with the automated *.exe installer, and having "Europe all" provided in one product/tile-set...
Over here many, many riders with older, still perfectly working GPS/satnavs using OSM...
Other users with different interests (MTB, climbing, skiing, hiking, geocaching...) use specific OSM mapsets (like with elevation model) on current GPS units/models...
I've no idea how alive the OSM community is over there in the states... nor if there is any group/forum specialized on this open source project who could provide more/detailed support...
I've also no idea about which step doesn't work on your end...
While we were starting this debate, I installed a new map-set from above source right here on this Win11_64pro PC at my office... flawless...
I'd be really surprised if your edition of Base Camp (or even the Zumo) has like a "geo-block"...
Since Garmin (again) has decided to discontinue a map-series (NT maps are superseded by their NTU maps), I'll also have to feed my GF's Zumo 220 with OSM on a micro-SD to keep it up to date...
Bound by the <4GB limit of the FAT32 system on the SD card, I select the "general area/countries" of tiles we intend to travel in MapInstall while monitoring the "storage bar" at the bottom...
(even worse on my Quest-I with only <420KB internal memory, requiring to select a "corridor" of map-tiles along the planned routes...

)
When searching for genuine "GARMIN City Navigator NT Benelux-France, Micro-SD, suitable for navigation devices" they're avail, starting at like € 40,- upward...
But I can't see which year, thus how current they actually are... likely half of the roundabouts or bypass roads are missing...
i.e.
Garmin 010-11043-00 Maps of France and Benelux on SD-Card/microSD: Amazon.de: Electronics & Photo
www.amazon.de