This paper presents an experiment which focused on determining if a telecollaborative project work would help enhance students' foreign language skills and cross-cultural competence. Students from Igor Sikorsky Kyiv Polytechnic Institute and the Polytechnic University of Valencia worked together during the fall term in 2020, in which 56 Ukrainian and Spanish students were engaged in a telecollaborative programme -- 32 were master degree students at Igor Sikorsky Kyiv Polytechnic Institute, whereas the remaining 24 were bachelor engineering students at Polytechnic University of Valencia. Our students were engaged in a project work which consisted in the creation of a blog on the topic 'Sustainable Development Today'. The tools used in this project were mostly Google applications such as Classroom, Hangouts, Blogger, Drive, and Docs. In order to measure their progress, students took pre-tests before the project started and a post-test after its completion. These tests focused on assessing learners' language competence in English and also their cross-cultural competence. The language test used was designed by Cambridge University Press, whereas the cross-cultural test had been created by the Organizational Behavior Group (Piasentin, 2012). The latter focused on learners' willingness to engage, cognitive flexibility and openness, emotional regulation, tolerance of uncertainty, self-efficacy, and ethnocultural empathy. As expected, the students who participated in this virtual exchange programme enhanced their competence on both foreign language cross-cultural competences by taking an active part in the telecollaborative project work.