I'm in a different province and made the choice to send my very bright, speaking in full sentences at 16 mo, multiplying and reading well before age 5, dd to French immersion.
I figured I could and would supplement her curriculum at home with extra opportunities and materials that would challenge her abilities, but I couldn't give her a good accent in our country's second language at home or through later language courses.
My sister and I were in gifted programs, 25-30 years ago, so very different now, I'm sure, but looking back, I do not feel that I learned much or more from them than from learning opportunities I pursued on my own. I did not feel that I benefitted particularly growing up with the label "gifted" either. But that would be another thread. Maybe the OP might benefit from asking her question in the "Gifted" forum?
DD is now 12. Her accent is beautiful and she has a strong foundation in French and Spanish (the third language was introduced in grade 2, also taught in immersion classes). She also reads at least a full-length novel a day in English or French between schoolwork- and writes and spells at a high-school/ college level in English, despite the fact that her English teachers are francophones. ie. she is strongly gifted in English, which is not well supported by her FI school, and she could use more challenges generally..
We are going to be homeschooling her for grade 7 to give her a chance to pursue her some of her own interests, which include learning German and pursuing some sports and theatre interests, and traveling to visit family abroad. We plan to use the provincial English language curriculum for core subjects for the first year and let her pick options. If it doesn't work out, we'll return her to the FI program, I think.
Our decision to homeschool is more related to our desire to let our daughter take more control of her education and our understanding of her independent learning style, than it is to discontent with what the FI program is offering her in particular. I would never consider pulling her out to move her to our local gifted program, as I know of two families who have pulled children out of that program due to bullying and physical aggression by other students against their children, and I also know that the charter gifted school has suffered some growing pains and lots of staff turnover. I'm sure these problems are not universal, but I believe it is true that some gifted children may have other exceptionalities that could lead to behavior and classroom management problems if not properly supported. I think it is important in evaluating *any* program, gifted or FI or mainstream, to watch for any warning signs of these kinds of issues.
I don't regret the decision to start dd in FI and we have, in fact, started our 5 yr old, who is also very bright, in FI kindergarten this year.
A point was made earlier that FI classrooms have the range of behavioral/learning issues plus French on top. I actually find this not to be true, at least not in my dd's school, to the point that it feels discriminatory and really bothers me, actually. I have never seen a disabled child requiring an aide in any of her classrooms and there are several that I know of in English language schools locally. There is a very high number of girls compared to boys in her classrooms (the other local school, non-immersion, has a very high number of boys compared to girls).
I have a son in FI kindy now and another who will start in a couple of years and I will be watching very closely to see if it is the right environment for my boys, or if the educational style seems biased towards supporting girls. So far, so good, with my older son.
I think it may be partially self-selection on the part of parents. A friend lives across the street from the FI school my dd attends but did not enroll her speech-delayed child in FI, figuring that if she was challenged in her first language, why attempt a second language on top of that? But I also believe that this FI school does not encourage or support parents of students who are having difficulties to remain in the school. I know of parents who have pulled their children with learning disabilities or behavior problems out of this school after conflicts with teachers and no support from the principal. It is almost as if there is an agenda to get rid of "troublemakers"
YMMV. I think that advice for you,, OP to check out both programs in person now is wise.
I think in your shoes, assuming the FI program looked like a good fit, I'd start my child in FI and investigate options to transfer to the gifted program later on.