The rise in comparable to that of recent years, Pascal Brice, the head of the Ofpra refugee agency, told the AFP news agency.
The number of applications rose 17 percent in 2017, for the first time going over 100,000 for the whole year.
This year's rise is largely explained by faster handling of applications by préfectures, who handle the first stage of the process.
The main countries of origin were:
Afghanistan: about 6,000 applications, many following a recent trend of applying in France, where 80 percent are accepted, after being turned down in Germany and northern Europe;
Albania: 3,800 applications, down from first place last year after an Interior Ministry drive to reduce demand;
Georgia: 3,800 applications, which have little chance of success, Interior Minister Gérard Collomb having complained of an "explosion" in demand, blaming it on the ending on an exemption from short-stay visas introduced in March last year;
Côte d'Ivoire: 2,800 applications;
Guinea: 2,800 applications;
Sudan: 2,600 applications.
Despite the seven-year civil war there, Syria is only in ninth place, with 2,000 applications, largely made when Ofpra teams visited neighbouring countries.
Since June Ofpra has sent teams to Mediterranean ports to interview migrants aboard rescue ships such as the Aquarius, which was denied landing rights by Italy.
France is pushing for a EU-wide agreement to share out refugees picked up in the open sea.