Neo4j only supports Java natively. The only other way to access is through the REST API, or exposing something on your own.
Things like RexPro are a good alternative, but it's still using some type of RESTful endpoint, and I do not see a C++ binding.
Can you share what you need the native Neo4j API for? Is this something that can be accomplished via Cypher or Gremlin, and you just have the data shipped back to you via the RESTful endpoint.