possible to go to Canada and also see Europe on the cheap?
Upvote:2
Anything is possible but there are three difficulties with your plan:
Luxembourg is quite expensive and not a big transit hub. It will be more expensive to get there and away than adding a layover in Paris, Frankfurt, Amsterdam, Rome or Madrid.
You can easily get to Belgium, Germany and France for a day trip and those three countries are not all that expensive (for Western Europe that is) and you can save money by taking your lunch with you instead of eating out. Unfortunately, Arlon, Thionville, and SaarbrΓΌcken are not the prettiest or most interesting places in Belgium, France, and Germany.
You do need a different visa, which requires some time and money to obtain.