Alonso was quick out of the garage before the rain came to post a lap of one minute and 18.887 seconds, nearly half a second clear of Ferrari driver Charles Leclerc.
Red Bull's Verstappen was third quickest ahead of Mercedes' George Russell but caution took priority over pace in the conditions.
Lewis Hamilton, second fastest in the first session, posted only the 13th fastest lap in the second and spent much of it in the garage as engineers tinkered with his car's suspension.
Verstappen and Ferrari's Carlos Sainz almost collided in traffic as cars jammed the track before the rain, but Lando Norris was the first to come to grief when the weather changed as he slid his Aston Martin into grass and gravel at turn one.
Verstappen earlier topped an eventful first session (FP1) under blue skies, lapping in one minute, 18.790 seconds, nearly half a second quicker than second fastest Hamilton.
Two red flags disrupted the session.
It was halted midway through due to a GPS failure, which organisers said made teams unable to monitor car positions and closing speeds.
The second red flag cut the session short by a few minutes as Williams rookie Logan Sargeant came to a halt on track-side grass with an apparent power failure.
Sargeant did not emerge from the Williams garage to post a lap in the second session.
Verstappen's teammate Sergio Perez was third quickest, with Alonso fourth.
Verstappen finished FP1 with a bit of drama, taking a big spin at turn four to ruin his tyres.
Leclerc and Sainz were fifth and sixth quickest with McLaren's Lando Norris seventh.
Alpine's Pierre Gasly was eighth fastest ahead of Russell.
Home hero and McLaren rookie Oscar Piastri was 12th in FP1 and 14th in FP2.
Haas's Kevin Magnussen, the slowest of the 20 cars in FP1, skidded into the gravel, while AlphaTauri's Yuki Tsunoda also locked up at high speed to take a big slide through gravel midway through.
