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The phrase "je vous en prie" (zheh vooz-ahng pree) uses "vous," the formal French "you," indicating it's a more formal way to say "you're welcome." This phrase is appropriate in more formal situations, or when you're thanked by an adult who you don't know.  Also use this phrase when you're speaking to an adult who is older than you or in a position of authority. If you're traveling to France and can only learn one way to say "you're welcome" in French, this is probably the best one to choose. Although you may be overly formal in some situations, you never run the risk of offending anyone for being too casual if you use this phrase. In some situations, both you and the other person mutually help each other out. If that happens and they thank you first, you might say "merci à vous" (mair-see ah voo) to thank them in return.  For example, if you and a coworker or colleague you don't know very well have just finished working on a project together and they say "merci," you might respond "merci à vous." Since "vous" is used in this phrase as well, it's appropriate in situations where you don't know the person who's thanking you, they're much older than you, or they're in a position of authority over you. The phrase "c'est moi due vous remercie" (say mwah kuh voo reh-mair-see) means "it's me who thanks you." If a sales clerk in a shop assists you in selecting items to purchase and you thank them, you'll likely hear this in return. Often, this phrase is shortened to simply "c'est moi." The rest of the phrase is understood by French speakers. The shortened form is typically used in more casual situations, such as if you're talking to someone you don't know but who is around the same age as you.
Say "je vous en prie" in polite or serious situations. Use "merci à vous" after mutual assistance. Try "c'est moi que vous remercie" if someone helps you.