If you're referring to a single pot of money that exists to support Research and Development, you would typically refer to that as "The European Defence Fund" as "entire EU defence fund budget" would be interpreted differently.
True, but IMO it's a bit misleading because you were using as a point of comparison something that sounded like the military budget of Europe without specifying that it's something completely different (that people probably never heard of — at least I didn't and neither did my grandparent). I'm not saying it's intentional or anything, just wanted to point it out.
The EU defence spend in 2022 was €240 billion.