Learn French: Bon appétit, Madame ! - Enjoy your meal, madam!

In French, you don't literally tell someone to "enjoy" their meal. Instead, you wish them a good appetite (bon appétit). It is the standard polite phrase to say right before eating.

Do I pronounce the "n" in bon here?

Yes! Normally, the "n" in bon just makes the "o" nasal and isn't pronounced as a hard consonant. But because the next word (appétit) starts with a vowel, you make a sound link called a liaison. You pronounce the "n" so the two words flow together, sounding almost like "bon-nappétit".

Is it normal to say Madame without her last name?

Yes, it is very common and polite in French. While it sounds a bit strange in English to just say "Mrs." or "Madam" to a stranger, addressing a woman simply as Madame is the standard way to show respect in French.