This video guide at Seeking Tech will show you how to find and capture all the Petanks in Clair Obscur: Expedition 33.
In order to capture one, you have to chase it to its mantle, which is usually located nearby. Afterwards, you need to defeat it in battle.
While the fights can be somewhat tricky, you can rest at a nearby flag to get the Petank to respawn so that you can fight it again. Of course, you can always come back to the same spot after you level up if you are having issues trying to beat this enemy before it could run away.
You can find the video guide, along with the time stamps, below:
0:00 Ancient Sanctuary (Entrance) Petank
3:50 Esquie’s Nest (Entrance) Petank
7:13 Stone Wave Cliffs (Old Farm) Petank
9:15 Forgotten Battlefield (Battlefield) Petank
10:49 Sirene (Dancing Classes) Petank
15:10 Sirene (Crumbling Path) Petank
18:43 The Monolith (Tainted Cliffs) Petank
23:27 Frozen Hearts (Iced Heart) Petank
25:04 The Reacher (Ladder Area) Petank
27:36 The Continent Chromatic Petank
31:04 Endless Night Sanctuary (Warrior’s Route) Petank
33:16 Flying Manor Petank
36:03 Isle of the Eyes Petank