Sino-French kid in China: Passport, Entry&Exit Permit, Names

[Livlander]

Hi there,

Here is the situation I wish I can get advice about.

I am French, my wife's Chinese, and we have a baby girl born in June. She got her French passport right away, then got her Chinese Exit & Entry Permit, allowing her to leave China.

1. Her French passport shows her French family name (mine) and given names only, and of course has a passport number.
2. Her Exit &Entry Permit only shows her Chinese family name (her mother's) and Chinese given names (totally different from French given names), and has a specific Exit&Entry Permit number.

Questions:
- When making the plane ticket reservation from Beijing to France, which document should be used to avoid trouble when at Beijing airport: Exit & Entry permit or French passport?
- Whatever the document registered with the air company may be, will the Immigration/Security control request the other document as an additional control, which may generate trouble since the names do not match? Only picture and date of birth do match.
As a matter of fact, if we assume we first use her Exit&Entry Permit, they may wanna check she has the right to enter France, which would be given by her French passport...

Thanks in advance for any advice or thoughts about this issue.

Didier