I thought you would meet him next Monday. Would is the past tense of Will. While will refers to the future. For example: I will meet you next Monday. Would is also use for uncertainty, conditionals and something that is possible. Examples are: It would be very nice if I could see you next week. (possible results) If I had not lost my phone, I would have given her a call. (condition) So WOULD is the correct choice

"I thought it was Monday" would be the best way of expressing this. There is no doubt about the fact that your friend is planning on meeting the other person, it is only which day of the week that is in doubt.