Hmm, as several other posters here I am an immersive reader (missed my bus or train stop several times because of a book) so I cannot really imagine your problem.
However, my suggestion would be to get your hands on audio material for learning foreign languages. There may even be pod-casts or other such web resources. Later on, once you acquire a basic vocabulary, you may also listen to pod-casts in that foreign language that are on whatever subjects.
This may work as the brain may be "puzzled" enough by the strange words to not treat the sounds as just "noise". It may be that you will not make progress in learning the new language at the same speed as people who focus on it but your main intention is different.
This gives me an idea. (Sorry, going OT...
What would happen if one would try to read English and listen to French or vice-versa (assuming you know both of course)?
I would assume that reading and listening (to two different texts) in the same language will result in sub-optimal absorption of information from one or even both sources (I for one cannot multi task). But reading in one language and listening in another? How would that work?
I'm bi-lingual. When I speak or listen in a language I also think in that language. What if, to some extent
, the brain uses different areas to "think" for the different languages? Could it be that the brain could handle information from two sources easier if they are from different languages?