Dating someone who speaks broken English

Hey, folks!
I was wondering if anyone here has experiences with dating someone with no real shared common language.

I (29F) met a guy (30M) last weekend. He came up to me at a bar, but I was already eyeing him for a while at that point since he was ridiculously attractive. When we started talking he had a hard time finding the words, but I assumed it was just the alcohol or the nerves, and thought it was kind of cute.

We’ve been texting for a few days now, and we’re talking about going out some night this week, but by now I have realized that he barely speaks English to the point where I often have no idea what he wants to say.
My English obviously isn’t perfect either since it’s my third language, but I never had an issue communicating while dating before.

I’m a little torn about what to do here, since I’m so attracted to him physically, and he seems like a nice person and all, but I feel like going out would be super awkward if we don’t understand each other.

Has anyone here ever been in a similar situation? Should I cut contact now before the physical attraction distorts my view of this? Wouldn’t it be a little too hurtful to tell him he doesn’t speak good enough English to date?
If any of you ended up dating someone like this, how did that work?

Any insight would be appreciated.