My kids attended a French language immersion school from PreK through part of elementary. Eldest went through 4th grade, middle kid through 2nd and youngest through 3rd grade. They left for a mix of financial reasons (couldn't keep paying tuition, especially when eldest went off to college) and class size reasons.
I noticed on your other thread you mentioned very small schools. While their immersion school was not small, it wasn't big either. PreK through 4th probably had 30 kids per class (split into two sections). 5th through 8th grade had as few as six kids (school only goes through 8th). Because the middle school grades are so small, the school could not offer the range of ECs that my kids wanted. Of course, your child is only three, so I wouldn't concern myself with the small class size at this point.
The immersion school they attended was not specifically for gifted kids, but there are plenty of kids there who are very likely gifted. For example, my eldest kept in touch with her classmates, and at least 25% of the class now attends an Ivy. The other 75% are attending well regarded colleges, though not elite schools. My eldest is now on a study abroad semester in France, as a sophomore. Typically they make kids at her college wait until junior year, but she is fluent (and also has junior standing, but that is a different discussion).
My older two were not identified as gifted until 7th grade, so our decision to send them to the language immersion school had nothing to do with being gifted. My youngest is in 5th and we have not had her tested. The immersion school was good for them as they were surrounded by bright kids (you'll have to evaluate your immersion options to see if this is true there). More importantly, they learned another language when they were young. It is much easier to pick up a language as a little kid, and my older two report that taking another language later (German for eldest, Spanish for middle kid) was easy due to the immersion experience.
