When it did get under way, it progressively dried to the point that the drivers were able to run slick tyres for the final five minutes of the session.
Norris set the pace by 0.328secs from the Ferraris of Carlos Sainz and Charles Leclerc.
In the second session, Alonso ran consistently at the front as the track had a brief dry period for 15 minutes or so at the start before rain started again.
The two-time champion said: “A tricky Friday for everyone. Not many laps in either session.
“No proper laps in dry conditions or in wet conditions, but it could be like this in qualifying and race. We need to be sharp tomorrow.”
Behind Alonso and Russell, the Spaniard’s team-mate Lance Stroll was third fastest, from Leclerc, RB’s Daniel Ricciardo, Haas driver Kevin Magnussen and Lewis Hamilton’s Mercedes.
Hamilton, who with Michael Schumacher is the equal most successful driver in Montreal with seven wins, said: “It felt great. I was just raring to go every second. This is a track where it’s building blocks, about getting as much time in the car and understanding both conditions and the changes they have made to the surface and the run-off areas.
“The car was feeling strong. I thoroughly enjoyed it.
“The circuit is amazing. It is one of the best circuits but this was an odd day, like a summer’s day in the UK. It was summer this morning then it rains with huge hailstones, then sunny and hot and humid and then rain again.
“I feel really confident out there but we won’t know until we get out there on Saturday but on either conditions I felt really strong today.”
Despite the conditions, only one driver crashed all day – Sauber’s Zhou Gunayu lost control through Turn Five in the first session and broke his front suspension.
Leclerc won a cheer from the crowd at the hairpin when he did a 360-degree spin in the second session, to no harm.
