The unemployment rate rapidly increased in the 70s, then stabilized at around 10% before starting to rise again in early 2000.

Notes: Adverbs typically go before the verb in English, though they can go after the verb sometimes, in this instance putting it in front of the verb felt stronger. (I speak English natively, so I don't really know why, I just know how it feels.) If you say it aloud this way, you should put emphasis on the word rapidly, and say the sentence slightly faster than if you say "increased rapidly." 

Also, "early 2000" sounds weird, because it could be mistaken for "the early 2000s" describing the first part of the century, or as "early 2000" describing the first part of the year. I would change this to the month or the season of the year that it changed, so it would be "in the (season) of 2000" or "in (month) of 2000." Your wording was 100% grammatically correct, but to someone who speaks English natively, to two are easily accidentally interchangeable.

I do not understand the second paragraph. Are some of these nouns proper nouns? If so, what do they mean in context? I speak a bit of French, so could you maybe write down what you wanted to say in French, in case there was an error in translation?