I am not sure if she is well-known in Asia, but Patricia Kaas has a deep, expressive voice that captures the spirits of French chansons and made her one of the most successful female singers in Europe. One of her trademark songs is Une Fille de l'Est, a song about Kaas' home region of Alsace-Lorraine in eastern France.
Kaas was born in Forbach, Alsace, a small town right on the Franco-German border and she starts singing at a local pub at a young age. Besides French, she also sings in English, German, and Russian. Some of most well-known songs have been adapted by other artists in recent years, such as J'ai peur de tout: (P.S,: For those with weak hearts, be warned that Patricia Kaas' music videos do not shy away from some highly sexually suggestive scenes)
A beautiful song: Il me dit que je suis belle, which translates roughly as 'He said I am beautiful'. The Youtube video I choose to embed here is not the original music video, because the original version is so sexually charged that embedding has been deactivated on Youtube.
Another of my favourite: JE VOUDRAIS LA CONNAITRE
All Music Videos Courtesy of Youtube