Hello, as far as I could see from a screenshot everything is correct. You put this email shop@chien-heureux.com in the field Send to, so this is correct.
We will need your WordPress login and password to check it out.If I do a test via the contact form of my website it doesn't work.
Can you test on my site please.
https://chien-heureux.com/contact-us/
Sorry I'm not woken up this morning.
I'm waiting for an automatic reply.
But there is none on the contact page.