How can I load this file into an NUnit Test?

You could specify in the properties of the file to be copied to the output folder and inside the unit test:

string text = File.ReadAllText(Path.Combine(TestContext.CurrentContext.TestDirectory, "TestData", "126.txt"));

As an alternative you could embed this file as a resource into the test assembly and then:

var assembly = Assembly.GetExecutingAssembly();
using (var stream = assembly.GetManifestResourceStream("ProjectName.Tests.IntegrationTests.TestData.126.txt"))
using (var reader = new StreamReader(stream))
{
    string text = reader.ReadToEnd();
}