This question has been on my mind all day and a few things occurred to me.
Before Bryan said the line, the abductor had been on the phone for several seconds, so if it was a kidnapping, he had plenty of opportunity to demand a ransom. This leaves likely possible scenarios:
- The abductor is just some petty thug, some muscle hired to do the actual kidnapping, and the guys boss would later contact them to demand a ransom
- The abduction has nothing to do with ransom, in which case it is likely to be either:
- Something nasty with rape and murder
- Kidnapping for use in sex-trafficking
If it is the first case and the guy was just a petty thug, then Bryan’s threat had a small, but decent chance of scaring the guy into abandoning the kidnapping and running away.
If it is not about ransom and it was the first sub case, then Kim was as good as dead by the time that Bryan has a chance to even get to France. In this case, skip to the end.
If it is the second sub case (sex-trafficking), then he knows that even if they treat her like crap, they are going to keep her alive since they don’t usually cater to necrophiliacs. Remember that Bryan is a retired CIA agent so regardless of what department he was in, he has likely learned quite a bit about the sex-trafficking “industry” and how it works. He likely understood that they would be somewhat professional and thus, prefer to just rent her out or sell her than to attempt to arrange a likely-to-fail ransom exchange.
Either way, he had nothing left to lose (his ex-wife is married to another man, he is retired, and now his daughter has been kidnapped). What else is he going to do now, read the Harry Potter books? Of course not; he has nothing to lose and nothing to do anymore, so he may as well spend the rest of his life tracking her down if possible and hunting the kidnappers down and killing them.
No doubt that at the back of his mind, he considered that he may very well never see her again. He is not the type of person to play the victim and just roll over, so he of course he wants to pull a Ransom and fight back.
I agree that warning them was bad. He may be around the world, but by telling them that he’s got skills and connections and is coming for them, he puts them on high-alert, especially with her. However, don’t forget that no matter how well he is trained to contain his emotions, his child was just abducted, so he feels fear and rage and cannot just think through every single angle and action in a couple of seconds.