According to the title of the video, which is all I looked at (my French not being that good), you are making a pate brisee which is a particular kind of pastry crust.
This pastry relies on solid fat in its construction method, so that it can be in little clumps in the dough. Then, it melts during baking forming a crumbly crust.
You will not achieve ideal results with any liquid shortening such as olive oil. Some viable options (which may actually achieve better results, depending on your desires) to substitute for all or part of the butter include:
- Hydrogenated vegetable shortening (such as the US brand Crisco)
- Beef tallow
Basically, any fat which is solid at room temperature (almost always animal fats, since typically only saturated fats are solid at room temperature) will do.
If you google "olive oil pastry crust", you will find recipes such as this one from Fuss Free Cooking which are not based on butter or solid shortening. You will get a different texture and outcome, but depending on your goals, you may find such as recipe to your liking. I cannot vouch for their quality, as I have not tried them. Obviously, they will have a different flavor from the oil rather than butter...