The two countries in a 1973 pact agreed to allow only flag carriers Korean Air and Air France to fly the route.
South Korea wants France to permit multiple airlines, so the second national airline Asiana can also fly the route. France has been reluctant to accept the demand, as it has only one flag carrier, Air France, officials said.
"Today's meeting focused on three subjects including our proposal to permit multiple airlines and increase flights on the Seoul-Paris route," a transport ministry official told Agence France-Presse on condition of anonymity.
He said France wants South Korea to accept a European Union Community Clause, which allows an EU member country to designate an airline of any other EU member as its national flag carrier.
Korean Air has opposed the EU clause, while rival Asiana claims it will boost the competitiveness of local carriers.
If South Korea accepts the clause, Asiana would also be able to fly the Seoul-Paris route.
Asiana says flights between South Korea and France are more than 80 pct full on average and there is a shortage of seats during high seasons.
"The clause must not be accepted as it will force the complete opening of our airline market to all EU member countries," Korean Air president Lee Jong-Hee said last week.