You have a decompressing GZipStream, so you need to read data from it. The easiest way is to wrap the GZipStream with a StreamReader which has a ReadToEnd method returning a string.
Something like:
string res;
using (var decompress = new GZipStream(inFile, CompressionMode.Decompress))
using (var sr = new StreamReader(decompress)) {
res = sr.ReadToEnd();
}
(using statements ensure that inFile is closed and any other resources are freed.)
NB this does assume that inFile contains text encoded UTF-8 or UTF-16. Binary content or other text encoding could cause problems (you can override the encoding with a different StreamReader constructor).