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You shouldn't have to use any adhesive, the surround provides an interference fit when all the stars align and the replacement glass is a perfect reproduction.
My experience is the glass tends to be a tad too large, so weatherstrip adhesive works well in that case.
Gents - while on the topic of rear view mirrors, I have gone to lengths to maintain the originality of my C3. BUT, the best thing I did was to buy a Gentex rear view mirror - frankly, I don't even know if they can still be bought and it took my a couple of hours to install - but, it has been a godsend for three reasons. First, it has an electrochromic (auto dimming) feature which is useful because a lot of unintentional morons drive close to my rear-end at night, trying to check out the car. It also has an outside temperature indicator (I put the small black sensor out of view in the lower intake area, running the wire to it through the speedometer firewall grommet) so that my wife can agree when the tops go back on in the cooler evenings (53 degrees for us); and, it has an electronic compass so that we can sort off know where we're going while cruising those beautiful backroads in the summer/fall because neither of us has much of a sense of direction, and if a spontaneous longer cruise happens, I don't need to worry about forgetting the Garmin.
Just a little valuable insight if applicable to your situation as this forum is for. Let me know if you have any questions.