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First of all, you have to be well prepared and have the propper gear : make sure that your sleeping gear doesn't get wet (sleeping pad and bag + pajamas and socks) and that you have enough water for the night / have a water spot near your camp (but not too close either in case it would attract animals, be wary of animal tracks).
By being well prepared you won't be stressed because of a potentially dangerous situation.
I spent my first night alone out there last september in France, had a whiskey flask while listening to my favorite podcast and I had a blast, even though I was dumb enough to go camp during the deers mating season and had one of those fuckers screaming all night near my tent...