Assuming you delete the right files the only thing you will lose is your friend list and friend code.
I'll go ahead and mention the exact folder locations:
All regions:
nand://data/id0/sysdata/00010032/
Japan:
nand://data/id0/sysdata/0002008D/
USA:
nand://data/id0/sysdata/00020096/
Europe/Australia:
nand://data/id0/sysdata/0002009F/
There is two saves you have to wipe. The main module which appears to be the same for all regions and the applet save data (that part is region specific)
Use something like godmode9 to go in and delete the files. Don't delete the folders. That's not necessary and may cause issues. ID0 equals the random string/letters the first folder in your data folder has. (this matches the ID0 folder on your SD card's Nintendo 3DS folder usually) That folder name will be unique to each user.
The file(s) you will be deleting have no file extension and usually have a file name of 00000000.
If after wiping this data your FC doesn't change, then the only thing that will change it is a new movable.sed seed.