France is one of the five permanent members on the Security Council, which will select the next Secretary-General.
Mr Key is likely to raise Ms Clark's candidacy, although it is the practice of the Permanent Five not to publicly reveal their preferences.
However, Mr Valls described Ms Clark as "a candidate of high quality".
"We are still at the start of the selection process and we will examine carefully all applications.
"For each of those, France will take into consideration political authority, management and linguistic skills."
About 10,000 French ex-pats live in New Zealand and another 8000 young people come here each year for working holidays.
Mr Valls said he hoped the visit would help strengthen the friendship and economic ties.
Prime Minister John Key has described it as a " short but important visit" for formal talks and events focusing predominantly on war commemorations.
There is an official welcome at the Auckland War Memorial Museum tomorrow, followed by a wreath laying and bilateral talks.