If Hamilton is successful in Sunday's race, which starts at 6.10pm UAE time he will regain the championship lead from Ferrari's Sebastian Vettel, who starts third.
"I was confident I could improve for the final attempt", Vettel said about his last flying lap that came up short. "There was time left on the track but I am really happy with pole".
"Over the long run I was able to play a little more and find some (driving) lines".
Charles Leclerc twice spun to a brief stop, while Max Verstappen drove his Red Bull wide on consecutive corners and Kevin Magnussen had a near miss with Sergio Perez.
The morning session ended with a scare for Sauber's Marcus Ericsson after his auto burst into flames when he spun out of control and slammed into a barrier.
A wheel then came off Sergio Perez's Force India auto at speed on the Mistral straight in the late afternoon.
Justices won't hear case of anti-gay marriage florist
Since the ruling from the lower court was unanimous, it seems unlikely that this second ruling would go in Stutzman's favor. It did not address generally whether businesses can decline services to same-sex weddings because of religious beliefs.
Ricciardo, victor of two races this season and still mulling his future options, was third fastest for Red Bull in the first session in 1:32.527.
The battle of Formula One's four-times champions has ebbed and flowed, with Vettel taking back the lead in Canada after Hamilton had to make do with an engine reaching the end of its life while rival teams had upgrades.
In demand Australian Daniel Ricciardo was third for Red Bull ahead of Finn Kimi Raikkonen and his Ferrari team-mate four-time champion and current leader Vettel. "You can see how close it is between us all".
Fernando Alonso, who was fourth for McLaren.
"That said, I have scored points in every single race I have finished, and hopefully tomorrow will be one of those Sundays".
"I feel very grateful for a solid weekend", said Hamilton after his victory at the Circuit Paul Ricard, the first French GP in 10 years.