Issues w/ 'search' in header area

Hi Support,

Enfold – Version 4.1.2 + Woocommerce – Version 3.2.5

We have the ‘search’ icon turned on in the header area of our website (https://maisonchristianfaure.ca) – when we type in a word and hit enter, no results appear – but if we slowly type in the word, the ajax kicks in and results starts appearing in the drop-down so you can at least see there are matching results. We have a woocommerce shop + blog posts.

Are you able to let us know if there is some way to fix this?
OR could we use a widget in the header to use the woocommerce predictive search instead? We have it setup on our main shop page and it is working – https://maisonchristianfaure.ca/en/shop/

Specific Test Scenarios when using search in header area:

1) When we type in ‘chocolate’ and hit enter, it returns no search results. This is the URL that is returned – https://maisonchristianfaure.ca/en/?s=chocolate&post_type=product. We noticed if we removed the post type results do appear – https://maisonchristianfaure.ca/en/?s=chocolate

2) But if we slowly type in ‘chocolate’, the ajax starts to work and results start appearing in the drop-down that you can click on.