Simple answer: no. But let’s consider it, anyway..
Tony Scott directed ENEMY OF THE STATE. As a scholar of film, he naturally would have both seen and appreciated Francis Coppola’s THE CONVERSATION.
Both movies deal with surveillance and paranoia vs actual menace, both personal and corporate/state.
And Gene Hackman is a standout star in each of these movies.
That is where the similarities begin and end.
The theory comes from the fact that Hackman plays an expert snooper in both films. His character also inhabits a near identical base of operations, with metal caged gates designed to block out prying signals. Now, those could be in joke nods.
Hackman here is used in the same way that Sean Connery could be seen as a late life James Bond in The Rock, by another name? A glory era on film, with second wind for macho, charismatic, convincing, versatile old school movie star actors, mentoring truly promising successors in organic story telling.
IE: this kind of movie connection comes from that narrow window of style and substance in the late 1990s – mid 2000s. Before the dark time. Before Nolan, Marvel, Star Wars et al (I enjoy each of those btw; I just loathe their now indelible legacy on how we view cinematic structures).
See, back in 1998, when ENEMY OF THE STATE came out? One could place a tactical in joke in a new movie, as briefest of brief nod to an old classic. A little something for the true experts who know their movies inside out, without labouring the point / showing off or isolating the casual fan.
If you did read a subsequent citation of said reference (back when one actually READ a movie and its criticism was an elite art) then you had a new discovery to make. The popular box office popcorn treat could lead you into more substantial waters, without itself ever trying to be some didactic sermon on politics or metatextual dissection of film.
So yes. Superficial similarity in what Hackman’s characters do and how they choose to deploy methods in the field: check. It is indeed there in Scott’s film and no doubt as a respectful nod to Coppola. But unlike today, it need not be an actual shared universe or a belated sequel / spin off / soft reboot etc.
It must also be said that ENEMY OF THE STATE is a more ‘fun’ movie than THE CONVERSATION. More style, less substance, though still clever and provocative. Scott entertains us with kinetic edits, immersive visual colour use and tech integrated to the very structure of the movie.
Coppola, by contrast? Well, he was riffing, experimenting and flexing his arthouse muscles between GODFATHER outings. Consequently, THE CONVERSATION, though excellent, is not an easy watch. You have to pay attention and it can be rather a drain, albeit a most rewarding one. It’s a textured, measured movie and that begins and indeed ends with Gene Hackman’s performance. And therein lies the answer here. These characters he is playing could not be more different. Yes, they both bug conversations.
But Tony Scott has Gene play a hard nosed, aggressive, adventurous, military man who not only understands the underworld he inhabits but actively embraces it. Coppola deploys Hackman to play a more quiet, shy, insular civilian. So unless the character changed entirely in 25 years or so, there is no way it can be the same guy and therefore these movies have only superficial, passing, thematic connection.
CASE CLOSED. END OF THE ‘conversation’ ? 😉