Noah Baumbach’s White Noise was the first film to be showcased at the festival, which runs until September 10.
The apocalyptic action film stars Driver as Jack Gladney, a college professor focused on the study of Adolf Hitler who lives with his wife, Babette (Gerwig).
Turner-Smith also co-stars with Marvel star Don Cheadle, who play Gladney’s colleagues at the university.
The British actress, who is also known for films including Queen And Slim, wore a long black, translucent dress, with jewelled detailing and red lining – and completed the look with elbow length green gloves.
Gerwig wore a simple black dress with a low neckline, while Driver and Cheadle donned tuxedos for the occasion.
Elsewhere, English singer Lott opted for a bold, red, sleeveless playsuit, and Clinton wore a flowing light-blue caftan.
Actress Julianne Moore, who is this year’s jury president, wore a black dress with explosive patterns and a matching cape.
Ahead of the White Noise screening French actress Catherine Deneuve was presented with the festival’s Lifetime Achievement Award.
The actress wore a floor-length red dress with padded shoulders to the opening ceremony.
Attendees also received a message from Ukrainian president Volodymyr Zelensky, who once again urged the world of cinema not to remain silent on the ongoing conflict in his country.