The Paris bid team said it would discuss introducing esports with the International Olympic Committee (IOC) before being named host in September.
Competitive video gaming will be a medal event at the 2022 Asian Games.
"It won't be possible to be an official discipline," said IeSF acting secretary general Leopold Chung.
"But to be a demonstration title within the Paris Olympics."
IOC president Thomas Bach said on Thursday it would be a "red line" for the organisation that no video games deemed to include "the promotion of violence" or "any kind of demonstration" would be permitted at the Olympics.
In October, the IOC said it is open to exploring the possibility of including esports in future Games, before stating at a November summit it "could be considered a sporting activity" but "must not infringe" on Olympic values in order to be recognised as a sport.
Chung said the support of the Paris organising committee will send a "stronger message" to the IOC that esports could be a demonstration sport at the 2024 Games.
"Paris would one day like to become an esports hub for Europe," he added.
"There are great engagement numbers, great fan numbers who live in France and especially in Paris, who would definitely want to come to an esports game."
The IeSF says its aim is to "work consistently to promote esport as a true sport beyond language, race and cultural barriers."
The organisation has 46 member nations and hosts an annual world championship.
Esports generated £400m in revenue in 2016, has a global audience of about 320 million. It is expected to generate more than £1bn in global revenue and almost double its audience to nearly 600 million people by 2020.
It is set to appear as a demonstration event for the first time at this year's Asian Games in Jakarta, Indonesia, before making its debut as a full event at the multi-sport tournament at Hangzhou, China in 2022.