Field Criterion does not take languages into account out of the box, however this is the intention behind $fieldFilters as exposed on search methods on SearchService [API].
See related issues, this is frequently requested from customers and community.
Issue https://jira.ez.no/browse/EZP-23397 implements field filters for Elasticsearch storage. LSE search lacks this and needs analogous implementation.
Note that it is possible this can't be achieved for FullText criterion in LSE.