Enchanté! The English verb "to meet" is very vague when talking about meeting people, but the five literal* French equivalents are much more specific, so you need to know in which circumstances to use each of them. This lesson should meet your expectations and help you improve your French fluency.
Faire la Connaissance
Use faire la connaissance when talking about meeting someone for the first time. There are two slightly different contructions:
1) Faire la connaissance de plus a noun or name:
- As-tu fait la connaissance de mon frère ?
Have you met my brother?
- Je vais enfin faire la connaissance de Jean-Paul.
I'm finally going to meet Jean-Paul.
2) Faire ___ connaissance, where ___ is a possessive adjective:
- Je suis ravi de faire votre connaissance.
I'm delighted to meet you.
- Connais-tu Sylvie ? J'ai fait sa connaissance hier.
Do you know Sylvie? I met her yesterday.
Literally "to reunite with each other," se réunir means "to meet with others at a meeting":
- Nous nous réunirons à midi.
We'll meet at noon.
- Où allez-vous vous réunir ?
Where are you going to meet? (Where's the meeting?)
Retrouver / Rejoindre
Both retrouver and rejoindre mean "to meet for an appointment or date":
Je te retrouverai/rejoindrai au restaurant.
I'll meet you at the restaurant.
Quand va-t-il nous retrouver/rejoindre ?
When is he going to meet (join) us?
Rencontrer, which literally means "to meet again," is used to refer to meeting someone accidentally or running into someone:
- J'ai rencontré ta sœur en ville.
I ran into your sister in town.
- J'espère ne pas rencontrer mon ex ce soir.
I hope I don't run into my ex tonight.
*This article covers only the literal translations; however, there are a number of figurative equivalents like meet your maker, meet your match, etc. You'll need to consult a French dictionary for those.