In a world increasingly globalized, multiple language skills can create more employment opportunities. Several countries include language training programs in active labor market programs for the unemployed. We analyze the effects of a language training program on the re-employment probability and hourly wages of the unemployed simultaneously, using high-quality administrative data from Luxembourg. We address selection into training by exploiting the rich administrative information available, and account for the complication that wages are "truncated" by unemployment by adopting a principal stratification framework. Estimation is undertaken with a mixture model likelihood-based approach. To improve inference, we use the individual's hours worked as a secondary outcome and a stochastic dominance assumption. These two features considerably ameliorate the multimodality problem commonly encountered in mixture models. We also conduct sensitivity analysis to assess the unconfoundedness assumption employed. Our results strongly suggest a positive effect (of up to 12.7 percent) of the language training programs on the re-employment probability, but no effects on wages for those who are observed employed regardless of training participation. It appears that, in the context of an open and multilingual economy, language training improve employability but the language skills acquired are not sufficiently rewarded to be reflected in higher wages.