Speaking to the BBC, chief executive Gwendoline Cazenave said "bottlenecks" are beginning to appear in stations due to post-Brexit border checks and current levels of border staff.
The operator is currently running 14 services a day between the English and French capitals, compared with 18 in 2019.
Cazenave warned the company may not restore some services which were suspended last year due to the problems.
"The thing is now we are not able to run the same transport offer as what we had before in 2019, because of bottlenecks in stations," she reportedly said.
