My mom and I had a "Taste of France" trip planned for June, but considering all that is going on in the world, the trip was cancelled. We booked through Explorica and finished our payments. We will be getting our money back, and we are wanting to plan our own trip. The trip was originally planned by my culinary teacher, so we had no say in the activities. This time we will be organizing it ourselves, but don't know where to start. We've never traveled abroad, so we were wondering if we would benefit more from exploring multiple places in France, or spending some time in Paris and then some time in Greece because my brother is stationed in the area. What are some opinions on the subject?

Doing it yourself will be best anyway.
Order some good guide books, Fodors, Fromers, Rick Steve’s, Eye Witness, etc.
Decide what you most want to see and do.
How much time do you actually have?
When are you hoping to go?
Where is your brother stationed?
Will you be allowed to visit him there?
Could he get leave to meet up with you someplace?

You need to provide loads more information before anyone can help you. See the questions above, plus:

How will you travel around?
What sort of budget do you have?

In addition to guidebooks, the internet is full of travel sites: e.g., start with the official website of Paris. There are also thousands of videos.

You are better off planning your own trip than going with Explorica, so that's good.

I hope you realize it will be months, at least, before you can travel to France. I'm not sure about Greece, but probably the same.

How long is the trip? What kind of budget do you have? Where are you flying from?

You could use the ideas that you liked from the trip you didn't take as part of your planning, assuming there were things that interested you in the culinary teacher's proposed itinerary.

The order I do things in is: set dates, buy plane ticket, make hotel reservations. Since you have never planned or traveled on your own before, I would suggest just doing Paris for at least one week. And if you have more time, add a couple day trips nearby, or perhaps one other city. If you want to go to Greece, than only do that.