You will surely be able to earn miles with a miles rewards credit card issued by a major bank and then redeem earned miles with any airline, including with KLM and Air France. Miles rewards credit cards will allow you to earn as many miles as you wish without caps or limitations. Earned miles will not expire. The redemption options are not only airline tickets, you will be able to redeem earned miles for all travel expenses like hotel rooms and rental cars. If you need cash, you can redeem for cash as well.
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All rates and fees, and other terms and conditions of the products mentioned in this article/post are actual as of the last update date but are subject to change. See the current products' Terms & Conditions on the issuing banks' websites.