Most introductions to the game say that you toss a coin, and the team that wins the toss throws the first jack. Another method is to hold out two closed fists and ask “Which hand is holding the jack?” But there is another traditional method that you might not be familiar with.
The traditional petanque “toss” is to take in hand the jack and a boule from each of the teams, and to toss all three into the air. When everything comes to rest, the team whose boule ends up closest to the jack wins the toss and plays first.
Here’s link to a Russian teaching video. It shows the traditional method starting at 1:03. The instructor says “You can toss a coin, of course, but the traditional method is…”
In the video, the instructor simply tosses the balls in the air in front of him, like you’d toss a coin. I’ve also seen players toss the balls over their shoulder, the way a bride throws the bridal bouquet.