* About half of French train journeys cancelled
* Paris-London and Paris-Brussels traffic back to normal
* Unions dispute government reform plan for SNCF (Releads with strike to go into third day)
PARIS, June 12 (Reuters) - French trade unions said they will extend for another day a strike that has caused the worst disruption to the country's rail network in years, following an inconclusive meeting with the transport minister on Thursday.
Half of scheduled train journeys across France were cancelled on the second day of the strike against a government plan to pull service operator SNCF and rail network RFF into a single holding structure but preserve them as separate entities.
Unions instead want the two to be fully merged into a single operation, as was the case until 1997, and for the government to take on some 40 billion euros of debt owed by the firms.
After meeting Transport Minister Frederic Cuvillier, unions said the strike would continue until 1900 Paris time on Friday.
"Once again, the minister has not heard the rail workers' demands. He has put a little ribbon around the reform, but there are no fundamental changes," SUD-Rail unionist Nathalie Bonnet told BFM TV after leaving talks with Cuvillier.
Gilbert Carrel of the CGT railroad workers' union said there was some progress, notably in a ministry proposal about new social dialogue at SNCF.
"We will take the time to reflect and to consult our organisations," he said.
Between 40 and 60 percent of cross-country trains operated on Thursday and just one third of local trains, but the Paris-London Eurostar and the Paris-Brussels Thalys lines had returned to normal, SNCF said.
SNCF workers fear the reform will hit their working conditions and argue that neglect of the tracks was a factor in a 2013 accident in which seven people were killed in a derailment attributed to a fault on a stretch of track just south of Paris.
They further argue that merging the two companies would avoid problems such as when SNCF acknowledged last month it had ordered 2,000 trains for an expanded regional network that were too wide for many station platforms.
The mix-up arose when the RFF transmitted faulty dimensions for its train platforms to the SNCF, which was in charge of ordering trains, local media reported.
The Ile-de-France region around Paris was hit harder than average by Thursday's strike with only one in three train journeys set to be maintained, SNCF said in a statement.
The rail reform is due to be debated in parliament next week. The unions were set to decide later in the day on whether to prolong the strike.
The rail strike disrupted traffic around Paris and other major French cities, with a total of 375 kilometres of traffic jams in the morning and slow traffic expected through Friday. (Reporting by Gregory Blachier; Writing by Ingrid Melander and Geert De Clercq; Editing by Mark John and Catherine Evans)