Hi David.
There is no apostrophe needed. The plural is Brandels, in English. (Or Brandles, if they did -le like you.)
Because, it's not possessive (and it's not a contraction). Exactly the same as the Trumps, for example, who also emigrated from Germany to Canada/America (but then back to Germany, then back to America). Whereas writing "the Trump's" with an apostrophe needs another word-- an object for the subject to possess, like, hotels. Trump's Hotel. But the family is Trumps, not Trump's.
Personally, I guess people get this wrong so frequently (because so many other people do too, but perhaps originally) because we see it in big letters on restaurants or other business signs, like "Maloney's" or whatever-- the point there is, it's HIS restaurant. Though he probably did it in error too. ;-)
Good luck with your research.
