the "R" in "Ver-" is pronounced like "R" in the "-er" in "Bruder" or like "R" in french?
To add some IPA to this discussion:
You would usually transcribe the r in that position (after unstressed e at the end of syllable or word) together with the e as either
[əʁ] or [ɐ]
The first one is with a voiced uvular fricative, but it is barely audible, not as strongly pronounced as in French.
The second version is what you'll more often hear (especially in the Rhineland, but it is very widespread), and what most people describe as "a", although it is produced more in the center of the mouth and very "relaxedly".
People who roll the r (typically in the south) might pronounce it yet differently, but unless you want to pass off as a Bavarian, I wouldn't worry too much about that.
And one more important point: in pronouncing things like Verein it is important to insert a glottal stop (a very slight pause) between the ver and the rest. So you have:
unless, of course, you want to have a French accent, then you have to leave out the glottal stop, which will automatically lead to a stronger pronunciation of the ʁ, because then it is between two vowels.
: if the next syllable starts with a consonant or glottal stop
: for non-linguists: a rasping sound which is created where you also pronounce k, and it is voiced like d or g or b, else it would sound similarly to the ch in Bach. It is also the r that the French have.
In German pronunciation there is no French r. The French r is produced back in the mouth cave, whereas the German r in Verein is produced in the front part of the mouth cave. The tip of the tongue touches shortly the point where the t is produced. I avoid terms of phonetics because not everybody has studied phonetics. At the end of a word as in Vater the r is not produced. The articulation is (almost) the same as in English father. Ah, I see there is a difference: Verein - verehren, verachten. In Verein you pronounce the r as if you had two words: Ve-rein. In verehren, verachten you pronounce ver- as English r at the end of a word, that is, you don't pronounce it. The next syllable is -ehren, -achten, not -rehren; -rachten.
Though I am German I discovered this curious thing just now. Wow!
PS I just read in a post above that Verein is spoken with a French r back in the mouth cave. Well, perhaps there are speakers who do that, but I must say I have never heard that or I would immediately ask Are you from France? I can only say that I speak Verein with a "frontal" r, that is, in the front part of the mouth cave with the tip of the tongue and I would say that most Germans do so.