The card might be valid elsewhere, that doesn’t mean that it‘s guaranteed to work with iTunes. And when you have a card on an account it has to be valid and pass iTunes validation, including when downloading free apps.
If it’s a debit card that might be why it’s being declined, not all seem to still be accepted by iTunes, and they might no longer be accepted at all in some countries. Have you got another card that you could try, or have you tried just logging into the account (not when trying to download something) and seeing if you can remove it ? If you can remove it you should be able to download free apps (and you could als try rexemtering its details from scratch)
For a card to have a chance of being accepted it needs to be registered to the same name and address (including format and spacing etc) that you have on your iTunes account, and have been issued by a bank in the country where you are (and therefore the country which is on your iTunes account).