Assumptions made in this answer
- State and Country/Territory Picklists have been enabled in Setup>Administer>Data Management and all values are converted
- Translation Workbench has been setup for the languages with users selected for each supported language. Translation Workbench documentation
Setup of Translations
Setup of Translation Workbench - got to Setup>Administer>Translation Workbench and enable this feature then setup translators.
Then setup the translations - unfortunately this will be a manual process as far as I can see, but is a one off activity as countries do not change their names frequently.
Apex/SOQL settings
To get the value in SOQL documentation link
Use toLabel() on regular, multi-select, division, or currency code picklist fields (any field that has picklist values returned by the relevant describe call), data category group and data category unique name fields or RecordType names. Any organization can use toLabel(). It is particularly useful for organizations that have the Translation Workbench enabled.