Within the field of second language research, it is well documented that language acquisition occurs primarily, possibly exclusively, during childhood as the brain loses plasticity after a certain age. It then becomes rigid and fixed, and loses the ability for adaptation and reorganisation, rendering language (re-)learning difficult.
What this means for your adopted child is that he or she will develop billingually with both languages for most of the early years of life provided there is aural imput from both languages and the child is allowed to interact in both. Some billingual children appear to develop slower than their one language peers, but the evidence seems to be that this is simply because they are “laying down the cognitive network” necessary to support more than one language. That cognitive network is a rich mixture of both lexis (words) and the suprasegmentals of a language (pronunctiation, intonation, accent, discourse structures, etc.) Imagine the inside of a baby’s brain encoding pathways for the billions of stimuli received for langauge; a bilingual child will create double. By the time the child is school aged, he/she will automatically choose the dominant language to interact in. If his classmates all speak English, so too will the child. But the neural network exists for both, doesn’t it? This is why many cognitive psychologists and Second Language Theorists argue that the child has the ability for multiple language skill.
There are other issues here. A child raised in a bilingual environment doesn’t automatically develop into an adult who can speak, read and write in dual languages. The higher cognitive skills like reading, grammar, writing and so on must also be developed. However, many in the field argue that children raised in a bilingual environment are at a strong advantage because of the neural networks created to process the suprasegmental aspects of the language. It is the main reason why adults, try as hard as they may, can never completely lose their accents when learning a foreign language. Other research in the field has indicated that the spoken fluency required to sound “native” drops off significantly after puberty. This may be biological or psychological, the evidence is unclear. However, it really doesn’t matter to answer your question.
I do have one question for you regarding the child. Are we talking about an infant here or a small toddler who has already been exposed to a first langauge?