Evidence of the effect that anxiety has on language learning is mixed @1991scovel_effect. There is no significant correlation between anxiety and language proficiency. There is weak evidence that a small amount of anxiety is beneficial for language learning, but high levels of anxiety are detrimental. Anxiety is a major obstacle to learning a foreign language
Further reading: Developing second language skills: Theory to practice Two measures of affective factors as they relate to progress in adult second language learning. Personality characteristics and second language learning in young children: A pilot study Affective, cognitive, and social factors in second language acquisition Avoidance behavior in adult second language acquisition