Infogrames bought not just the name, but the company [..] it is still the same company.
Not really, the "company" Infogrames bought and "continued" was merely Hasbro Interactive- and they themselves were merely an unrelated company that had purchased the Atari name and IP.
Quick rehash... the original "true" Atari Inc. ran into trouble following the 1983 US video game crash. It was split into arcade and consumer divisions; the former was "Atari Games" (later sold to Midway, who renamed it and eventually shut it down in 2003).
The latter was bought by Jack Tramiel and became "Atari Corp.", a legally separate company that nonetheless could still be seen as a spiritual continuation of Atari Inc's computer and console division.
Fast forward to the mid-90s, and all Atari Corp's recent products have flopped. The company is cash rich, but with no future, so Tramiel "merges" Atari Corp. with JTS, a second-rate hard drive maker. Since this is- in effect- just a means for him to transfer his investment to JTS, Atari Corp. basically ceases any meaningful operations at this point, remaining only a legal entity within JTS.
A couple of years later, JTS goes bankrupt, and Hasbro buys the Atari IP. No real connection with the original business(es) in any real sense, as there's nothing meaningful to continue by this point.
So, Hasbro weren't really "Atari" except that they bought the name and IP, and Infogrames aren't really either. Both successors that had any meaningful continuation of Atari Inc. (i.e. Atari Corp. and Atari Games) are both now long defunct with nothing left to continue.