Is there any advantage to picking up a foreign language as a child? That depends. It's important to be aware that bilingual children have significant extra hurdles in the early years of their schooling. Gifted bilingual children are underrecognized, and some are even mistakenly thought to be learning disabled.
But for those are able to become fairly proficient at two languages, this hard work appears to pay off one's entire life span. The study below shows that bilingualism reduces age-related decline in working memory and the slower response times! In other studies, there's a suggestion that "successful" bilinguals have stronger flexibility of thinking, higher 'creativity', and better problem solving ability. When you think about it, young bilingual children get much more intensive practice with inferences, and multiple word meanings.
Now that being said, the choice of whether to add a second language at a young age should be made individually. Children struggling with auditory processing, fundamental language disability, or working memory limitation should consider a foreign language waiver. Also realize that all languages are not alike. Some languages (like Spanish, Italian, or American Sign Language) are not as demanding phonetically or spelling-wise as languages like French.
Improved Cognitive Control Among Bilinguals
Bilingualism Press Release
Challenges with Young Bilingual Children