He has consistently denied any wrongdoing in a series of corruption cases dating back to his period as the capital's mayor between 1977 and 1995.
In an article published in Le Monde newspaper on Wednesday, the former president wrote he had made "legitimate and necessary" appointments to advise him and to help him revitalise Paris.
Only a small number of appointments out of the 40,000 city employees were in question.
"Who were these few officials? People to help clarify issues of substance for me - educational, social, economic, sporting problems," he wrote.
"It could also be men and women of quality, with all the necessary qualifications, but who were going through a difficult period professionally and to whom I wanted to give a fresh chance.
"And, finally, there were a very small number of aides who helped in the co-ordination and exercise of my functions."
Chirac's four chiefs of staff from 1983 to 1995 have already been placed under investigation.
The meeting with the judge focused on the organisation and functioning of the mayor's office. Another meeting, to deal more specifically with the jobs under question, will be organised "in a few months", Veil said.
It was the second time Chirac had been questioned since losing his presidential immunity. In July he was interviewed by a judge looking into other allegations of corruption.
The case he was questioned about in July concerned a similar affair in which Rally for the Republic party officials were said to have had their salaries paid by companies that had won contracts at City Hall.