The US500 was intended to replace the Indy 500 for the Champ Cars who had the better cars and drivers - and it failed miserably. Why? Because it didn't have 80 years of history behind it.
Not only can ASO likely protect certain trademarks - the yellow, green, polka dot and white jerseys, the red bib numbers, and even just licenced fonts and logos that are part of the branding of the Tour that are recognised worldwide - but they can also threaten to blacklist towns and cities that host the renegade race, or jack up the price if they want to get back in the good graces of ASO if the renegade race fails. It's a gamble that many places may be less willing to take in the circumstances.
Sponsor name races and things like that usually come with an inherent reduction in prestige compared to an 'official' national or regional tour because they're seen as entirely reliant on that sponsor's interest. As examples, look at events like the Clásico RCN which is, to all intents and purposes, a secondary Vuelta a Colombia, or the Clásico Banfoandes which was, to all intents and purposes, a secondary Vuelta a Venezuela (and also used to have a better course than the real thing too). These races have got some great winners - RCN has people like Martin Emilio Rodríguez, Rafael Niño, Lucho Herrera, Fabio Parra, Álvaro Mejía, Hernán Buenahora, Óscar Sevilla, Félix Cardenas, Fabio Duarte, while Banfoandes had Libardo Niño, José Rujano, Hernán Buenahora and Sérgio Henao - but they don't get pointed to on the palmarès the way the Vuelta a Colombia or Vuelta a Venezuela (or, hell, since Banfoandes always finished in Tachirá province, the Vuelta al Tachirá) are.
Notwithstanding that it's enshrined in French law to have the Tour on free to air TV I believe - something that a new race would not have, and unless it takes place at a different time of year, they are then going to be competing for airtime against a race which has an innate advantage not just in its century of history but that it will take up the capacity for cycling on free TV.