I think this new paper might be of interest to you.
The authors estimate the earnings advantage of workers that speak a second language, differentiating between native-born and foreign-born speakers. They evaluate this for 15 European countries, between 1994 and 2001. Their results are:
First, for
native-born workers with a tertiary diploma, using a foreign language at work is found to have
an unambiguously positive impact on their earnings (2% on average). Second, for foreign-
born workers, however, returns to foreign language use at work is highly complementary
to education. Foreign language users below the upper secondary educational level earned
significantly less (
−
8%) than those who use the local language at work. Third, with regard to
language types, a linguistically distant foreign language gives native-born workers the highest
wage premium, and EU official languages pays off the most for foreign-born workers. Fourth,
our results do not show that lack of local language knowledge of low-educated migrants causes
these results, as immigrants for whom the mother tongue is similar to the local language show
a similar pattern.
The authors also perform a calculation of the annual wage loss from low skill foreign-workers not speaking the local language (as wages belong to GDP, this could partly be seen as a GDP loss, but it's not a very decent general equilibrium exercise in my opinion). The results below:

Not only the article itself but the references of the article might be of interest to you. For example:
"Ginsburgh and Prieto-Rodriguez (2011) found that for native workers, English skills are well
rewarded in Northern Europe, but much less rewarded in Southern Europe (for example, less
than French and German in Italy, etc.)