Ian quite enjoys being "terribly boring and old-fashioned" yes. She is like "I'm married with a baby and a day job, and a house, and my wife wants a dog... I don't have the energy or desire to be interesting
." I do not know if Alexius took French, Spanish, or who knows what else. But Ian was involved, and would have been around for anything art related that her sister did. They could have met at something like that if Christine wanted to hang around a school event like that.
Teagan is currently moping because his ex-fiance used to be the local French teacher. (not based on your timeline, but suffice to say he's being sad about the relationship). Also he is fluent in French so he would get a kick out of talking to her about teaching and stuff in the break room yes. Teag likes to be friends with all his co-workers if he can, so they should spend time together yes.
Its alright, I was thoroughly amused at the Ian comment.