1st client, changing domain ?

I ve been doing SEO for years but mostly editing content and writing. Now that I m doing it as a side hustle, and got a client here is the situation. My client has been around for ages and has a 20years old domain. Problem: this is a French brand, composed of a full sentence and at least 3 useless word such as “and”, “or”. Plus, no word is relevant for the business, so not helping. Since we re working on changing the whole website wich is very dated and creating a new content strategy. I feel like the right way to go is to give him a better domain but I can’t wrap my head around how to do it and is it worth it ? Open to any advices if you been in the same case before.