Does anyone know of a beauty e-commerce site that carries YS Park brushes?

Hello, I’ll explain the context because it’s a bit specific. I’ve been running a small online store for about 8 months, selling professional hairdressing equipment, and I’m trying to properly optimize the product pages related to high-end brushes. Right now I’m stuck on something that seems simple but has been bothering me for about two weeks. The issue is that I can’t figure out whether I should use “the YS Park brushes” as an exact phrase in my title tags and URLs, or if it’s too English-heavy to be properly indexed on Google France. I checked the search volume and honestly it’s not negligible at all—people are clearly searching for this brand using the full wording with “the” in front. But I’m wondering whether my hosting setup (I’m on OVH shared pro hosting) could have any issues with URLs in English mixed with French content. My CMS is WordPress with WooCommerce, and the slugs automatically generated by my SEO plugin (Rank Math in this case) tend to strip small words like “the”. So my product page URL might lose that word, and I don’t know if that has any impact on ranking for that exact query.
Has anyone dealt with this kind of situation before, especially with English brand names on a French-language website? Do you keep the full brand name exactly as-is in your page titles, or do you adapt it?