SHA-256 Hash over multiple SHA-256 Hashes I am trying to implement a checksum over multiple files. 
We can assume, that i have a package containing N files. I want to identify such a package uniquely by following calculation:

SHA256-Hash over every file.

I save the result bytes of the hash-function for every file.

And then i calculate the sha256 hash over the concatenated file-hashes.
The reason, why i hash the file-hashes again is, that i want to provide a shorter footprint of the whole package. 

From my point of view this should be enough to identify a package. But my knowledge concerning cryptography is really limited at all - so i wanted to ask the experts.

Thanks in advance
Yes, this is fine for verifying that the file contents match the original. You are basically using a hash list. As long as SHA-256 is collision resistant, there is no way to find a hash that would be ambiguous and refer to two or more known file sets.

In addition to the potential issues mentioned in the comments, storing just the aggregate hash value leaves you with no way to figure out which file failed to match. That is why it is common to store the intermediate hashes as well to see which file would have to be e.g. downloaded again.