I don’t know whether there is such a version. At the risk of telling you something you already know, Century Gothic is a version of Twentieth Century (Lanston Monotype’s copy of Futura), redrawn to match the widths of ITC Avant Garde Gothic.
In that light, you might want to pick a different geometric sans with support for Georgian, and either harmonize that with Century Gothic in terms of size etc., or switch to that different geometric sans altogether.
I was curious to see if there’s maybe a Georgian version of ITC Avant Garde Gothic, but either Monotype’s filter is broken, or they offer zero fonts with support for Georgian. At least I get no results when filtering for Georgian. I’d expect to find at least Avenir Next Georgian.
Fontstand works much better in this regard: their filter returns Ping as a geometric sans with support for Georgian. Side note: Google Fonts and MyFonts offer language filters, too, but neither includes Georgian at the time of writing.
Both Ping Georgian and Avenir Next Georgian were made with local designer Akaki Razmadze.
Consider Typotheque’s Ping, which has a nice Georgian design in a wide range of weights by Akaki Razmadze. Also has the benefit of not supporting a Russian company whose CEO has publicly supported the invasion of Ukraine.
Comments
New Hero has some similarity to Century Gothic, and supports Georgian.
https://fonts.google.com/noto/fonts?noto.lang=ka_Geor¬o.script=Geor
https://www.paratype.com/catalog?languages[0][code]=lg-27&sortType=bestsellers
And here is the page for Futura:
Is it available only on request?