This is a pretty tough question. In the end, I think the language depends primarily on which language you want to know. That, in turn, depends primarily on the targets you find interesting.
If your interest in a database server is primarily to write something minimalist, such as for a "mobile platform" (e.g., smart phone) then the more minimalist language (C) probably fits your needs better. It lends itself better to situations where (for one obvious example) executable size matters more than flexibility or a rich feature set.
If you're thinking of a database server more along the lines of something that handles huge amounts of data, and is likely to run on relatively high-end hardware (that may well be dedicated almost exclusively to running that software) then C++ is likely to be a much better fit. C++ does have some cost (larger executables) for small programs, and many of the features it adds to C are intended primarily for keeping code organized in larger programs.
I would urge caution on one point: whichever way you go, be prepared for the fact that any language change tends to be at least a little painful for a while. Especially during the first few weeks, you'll inevitably find yourself thinking some variation of: "but why couldn't they just let me do X, like I'm used to?"
If you keep having those thoughts for a long time, it may simply be that Java is a better fit for your way of thinking and programming, and you'll be better off sticking with Java. I'd caution, however, against concluding that too soon -- like I said, especially for the first couple of weeks, and to a lesser extent for a few months, they're almost inevitable, even if you'd find C or C++ preferable given enough chance.
In fairness, I should add that even though I don't want to go back to them, there are a few features of languages I used to use that I still miss. I haven't written any Pascal in years now, but I still miss its built-in support for sets, and being able to do things like if X in 1..20. Even Fortran had a few features I still miss. I certainly don't miss those pieces enough to give any serious thought (any more) to going back to using Fortran at anything short of dire need, but ~30 years ago when I was first learning Pascal, I certainly did.
In fact, at one point I did actually try to go back to using Pascal after using C for a few years. Moving from Fortran to Pascal was almost euphoric. Moving from Pascal to C never felt nearly as positive, so after a few years of using C, I decided to go back to Pascal. That was, in a word, horrible. Despite some good points that were easy to remember, Pascal had far too many horrible shortcomings that I'd managed to forget (and hadn't originally noticed how huge of an improvement C really provided). Fortunately, it wasn't all wasted effort though: it got me out of the C rut enough that I never returned to it either, and moved on to C++ instead (though, unfortunately, I haven't found anything sufficiently attractive to get me out of that rut since, despite having really tried a few times).
