The Simple Future and Future Progressives Tenses have confused me from Day 1. Can someone clearly explain to me when to use one and when to use the other? For example, how do the actions in the examples below differ from each other?

I will study in Paris next year.

I will be studying in Paris next year.

I would really appreciate it if someone can enlighten me.
Hello, saveophilia - and welcome to English Forums.

Both forms show that the speaker feels certain that the event will in fact occur in the future.

Practically speaking, the progressive form usually expresses more interest, concern or enthusiasm – a closer emotional connection of the speaker to the event. The progressive, emphasizing as it does the ongoing activity, presents a more graphic image of the action.

In appropriate contexts, the progressive also exhibits its common function of presenting a background durative activity in he midst of which another future event will occur: I will be studying in Paris next year when I celebrate my birthday.
I think of them like this.

I will study in Paris next year.

Undifferentiated, featureless block of time. Reports a fact in a neutral way. Not very descriptive.

I will be studying in Paris next year.

Time filled with activity and detailed features. Reports with interest and enthusiasm. Descriptive.

___________________

When you see Fred in trouble, you can offer to help Fred.

Don't worry, Fred. I'll help you.

(You are communicating the fact of your willingness to help - not describing the help you will give.)

____________

If you have made a previous arrangement to help Fred do his homework, you can describe this to your friend Susan.

I'm sorry, Susan, but I can't take you to your dental appointment at 2 today. I'll be helping Fred do his homework.

(You are not offering help. You are describing the help you will be giving.)

Very briefly, the simple future is a statment; the progressive future is a description.

CJ
Students: We have free audio pronunciation exercises.
And CJ's last example also illustrates the use of the progressive as 'background durational activity', saveophelia:

I'm sorry, Susan, but I can't take you to your dental appointment at 2 today. I'll be helping Fred do his homework.

The 'helping' continues during the time that 'taking' might have occurred.
Good point. [Y]
Thank you for the input so far, CalifJim and Mister Macawber.

Hope you don't mind, but I have a follow-up.

Does it mean that, in a broad sense, these two tenses (i.e., Simple Future and Future Progressive) are interchangeable? Can usage of one over the other result in a grammatically incorrect sentence?

Again, I'd love to hear what you think.
Site Hint: Check out our list of pronunciation videos.
In a broad sense, either could appear in many sentences. However, as you can see from the earlier posts, usually one is more appropriate than the other.
saveopheliainterchangeable?
No, not in general, and not when you consider that the choice depends on the situation. Nevertheless, in some situations, either can be used. In that case it depends on how the speaker is thinking about the future situation.

saveopheliaCan usage of one over the other result in a grammatically incorrect sentence?
No. Absolutely not. Both tenses, if properly constructed, are grammatically correct.

There is a difference between a correct sentence and an appropriate sentence.

Suppose your friend has a pet cat.

You say, "Your dog is fun to play with".

Your response is grammatically correct, but inappropriate to the situation.

CJ