Red Bull vastly outperformed Mercedes at the Monaco and Azerbaijan street circuits but the German outfit has historically performed well at Le Castellet, with the team looking to find form again at the track.
Hamilton, however, had complaints with his car as Verstappen found answers from a difficult morning session, whilst the Red Bull long-run pace looked competitive at the end of the day's running.
Asked if he could top Mercedes across the weekend, Verstappen said: "Difficult to say but today was good.
"You never know what people will find overnight but also, the long runs seemed quite decent. For sure, it will be very tight and will not be easy."
Verstappen happy with Red Bull changes
Mercedes had secured a one-two in the morning session but Verstappen and Red Bull were able to make changes to hit back in the afternoon heat.
"I think we worked quite well, even during the session," Verstappen added, citing the set-up work done between sessions.
"Of course, FP1, I wasn't entirely happy, FP2 started still not amazing but I think the second set, the car felt a lot better, a lot more connected. It is still really difficult around here.
"The track is very open, it is windy out there so it is not easy to nail the lap. I think it is a good end to the day so we can be competitive tomorrow.
"It is quite gusty as well so one lap it feels alright and the next lap, it can increase so it is not going to be easy to judge your mid-corner speeds but at the end of the day, everyone has to deal with it and we will try to find a good solution around it.
"It is not easy and also the temperatures were quite hot."
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