Formal:
* Merci beaucoup, je suis très heureux/heureuse. (Thank you very much, I am very happy.) This is the most direct and formal translation.
Informal:
* Merci beaucoup, je suis content/contente. (Thank you very much, I'm happy.) This is a more casual translation.
* Merci beaucoup, ça me fait vraiment plaisir. (Thank you very much, it really makes me happy.) This emphasizes the feeling of joy and pleasure.
More specific:
* Je suis vraiment ravi/ravie de... (I am really delighted to...) You can follow this phrase with the reason for your happiness, e.g., "Je suis vraiment ravi de vous rencontrer" (I am really delighted to meet you).
Ultimately, the best translation depends on the specific situation and how you want to express your gratitude and happiness.