I am the first to say that anecdotal, non-scientific evidence has limited value. But I have a certain amount of experience and observation and have lived in many countries, usually among Americans, and we sent all our children to local French schools at least to age 12. They all speak French, one is married to a French man. The children of the others all go to French lycées or (in 1 case) a French nursery school. I speak only French to him, others speak mostly English to him; he doesn't speak at all yet (he's not yet 2) except for a few words, arbitrarily one language or the other: un, deux, shoe, car. (FWIW all the grandchildren other than the French ones are Swiss citizens, so their parents agree that they ought to speak at least 1 Swiss language. Especially my son who went to college with a Danish guy who spoke no Danish, only German, because his German mother divorced his Danish father when he was a toddler and both Denmark and Germany bar or limit dual nationality.)
I knew parents who sent their children to French schools and, one year later, despaired that they were learning nothing and took them out of the French system. Big mistake. Our kids started speaking French almost the first day of their second year of primary school, not before.
Ne vous en faites pas : votre enfant sait plus que vous ne le pensez.
There are books and books written on this. I started a thread the other day because I am interested -- out of curiosity not necessity -- in the learning of sign languages ( Swiss SL is based on the French system, as is ASL; British SL and German SL are different. Swiss German is close to Swiss French ). Anyway my point is that languages are easily learned before puberty, but not afterwards unless you have special aptitude. And while they are best learned beginning at age 0, anything before 5 is fine.
Many years ago my daughter was in a class in Ecolint, French Section, Geneva. One of her classmates was a Down child with a high level of ability. He spoke 3 languages.
Those are all anecdotes and should be read as such. I ask only that you take with some cynicism those who say that one should first be grounded in a single language before learning others. Whole generations of deaf children who were refused ASL because of the Second International Congress on Education of the Deaf (Milan Conference of 1880) where that view was established, were cheated: many never learned any language at all.
Look around you in Switzerland: I had a Swiss ancestor who, on stage, told jokes in six languages. In the 1920s Iowa and Nebraska tried to make it illegal to teach a foreign language to a child. Happily the Supreme Court threw that one out: Meyer v. Nebraska, 262 U.S. 390 (1923); Bartels v. Iowa, 262 U.S. 404 (1923). (Gov. Ma Ferguson is reputed to have said "If the King's English was good enough for Jesus Christ, it's good enough for the children of Texas!" She didn't of course, but you get the point. http://itre.cis.upenn.edu/myl/langua...es/003084.html
Good luck. Hope that helps.