"Nổi" here means "to rise" and "Tiếng" means "sound", and if you combine the two words into a compound word, then you get "nổi tiếng" (to rise in sound) aka famous (famous because people hear about you through the noise/tiếng" ). And yes, it's the same "Tiếng" used for languages.
Is there a rule or guideline about when to use "la" or "thi" ?
Would "toi thi rat noi tieng" work here?
"Thì" is more like a conjunction and can be translated as "then" as in "If a, THEN b". Like "Nếu nó muốn ăn thì nó ăn cơm." (If he wants to eat, then he ate rice).
"Là" is a copula, meaning that it connects nouns/noun phrases together. For example, "Tôi là người Việt" (I am Vietnamese), "Chị ấy là một học sinh" (She is a student), or "Tôi là bạn của chị ấy" (I am her friend).
Nổi tiếng is an adjective, and therefore cannot be used only "là". If you were to say "I am famous," you'd say "Tôi nổi tiếng," BUT if you want to say "I am very famous" you need to use an adverb of degree, such as "rất / rất là / quá" as in "Tôi rất nổi tiếng" / "Tôi rất là nổi tiếng" / "Tôi nổi tiếng quá". To know which adjective takes which adverb of degree most naturally, it'll take practice and time to get a feel for it. (Tôi rất nổi tiếng is the most natural sentence)
Hope that helps! EDIT: Made some corrections.