Well I have emailed, so no AIBU about it really 
Yesterday (Friday) 20 mins after primary school ended I saw a man at the bus stop outside the school. The bus stop usually has a large amount of teenaged girls waiting from the secondary opposite.
He was by himself indicating a bus had just been; there were no other adults or children around.
BUT. Earlier that morning the same man was at the primary sports day. He wasn't with a lady (for that read wife or partner), no reason why he should have been really, he might have been a single dad. BUT. He was chatting with another father, or rather he was listening as the other father waxed lyrical, pointing out his children and all their little friends, getting them to wave over.
Two months previous, I was on a train and he sat opposite me, with a French lady with two small girls (maybe 3 and 5). I assumed they were together, he knew their names. He carried their suitcase. I assumed the stilted conversation was because the lady didn't have English as a first language. I also assumed they were together because he was teasing one of the girls until she screamed in frustration. He was also asking lots of questions, but not in an obvious way, such as "when do you go home?" What are you doing tomorrow?" "is your Dad missing you?" - which of course I was oblivious to on the train because it was general chit chat.
See him at sports day and think it's that annoying wind up merchant again "oh, I didn't know there were little French girls at this school". There aren't any little French girls at the school and they were too young to be in the KS3 sports day anyway.
See him at the bus stop and think "hang on a min" gut instinct kicks in, something just isn't right here.
So I've emailed school with a full description, a set of circumstances and no accusations, because he wasn't actually doing anything suspiciously.
*disclaimer, I don't see a paedophile behind every tree, but I am a believer in gut instinct. I don't know why the red flags shot up when I saw him again. Probably because he was a bit of charmer, again not in an obvious way, he was just very good at ferreting out information from people.
Probably an entirely coincidental set of innocent circumstances and he is a listener rather than a talker.
Would you have emailed the school?