UnitTest strong exception guarantee
Do not attempt to put all the test criteria in one test. 
Make seperate (small) tests, which each cover one specific scenario.

If all tests pass, you know it is ok.
But make sure the tests do not depend on each other: that they can run in any order.

For the exception assert, it is better to use an Attribute on the test method: 

Update:

As Roland Illig mentioned, it is good to check that nothing was modified. 

Updated code fragment:

[TestMethod]
[ExpectedException(typeof(ArgumentException))]
public void SetFiles_FilesNotInTheSameFolder_ExpectedException()
{
    // 3rd call to SetFiles. Invalid

    // set to invalid structure (files not in same folder)
    // and expect throw
    // and no change

    var validParentFolder = @"c:\C:\muzică\folder1";
    var validFile1 = @"c:\C:\muzică\folder1\file1.txt";

    var invalidFile1 = @"C:\muzică\folder1\file2.txt";
    var invalidFile2 = @"C:\muzică\folder2\file2.txt";

    var fs = new Files();
    fs.SetFiles(new string[]
    {
        validFile1
    });


    fs.SetFiles(new string[]
        {
            invalidFile1,
            invalidFile2
        });

    // test that fs was not modified

    Assert.AreEqual(1, fs.FileList.Count);
    Assert.AreEqual(validParentFolder, fs.ParentFolder);

    Assert.AreEqual(validFile1, fs.FileList[0].Path);
}


Last remark, if this is working with real files, try to use stubs or mocks.

Update:

Below is compete test file, with the separated tests    

[TestClass]
public class UnitTest_Files
{
    private string expectedFile1;

    [TestMethod]
    public void SetFiles_Valid()
    {
        var fs = new Files();

        // 1st call to SetFiles. valid

        var expectedParentFolder = @"C:\work";
        var expectedFile1 = $@"{expectedParentFolder}\file1.txt";
        var expectedFile2 = $@"{expectedParentFolder}\file2.avi";
        var expectedFile3 = $@"{expectedParentFolder}\file3";

        fs.SetFiles(new string[]
            {
                expectedFile1,
                expectedFile2,
                expectedFile3
            });

        Assert.AreEqual(3, fs.FileList.Count);
        Assert.AreEqual(@"C:\work", fs.ParentFolder);
        Assert.AreEqual(expectedFile1, fs.FileList[0].Path);
        Assert.AreEqual(expectedFile2, fs.FileList[1].Path);
        Assert.AreEqual(expectedFile3, fs.FileList[2].Path);
    }    

    [TestMethod]
    public void SetFiles_Specialchars_Valid()
    {
        // 2nd call to SetFiles. valid
        var expectedParentFolder = @"C:\muzică\Diabulus in Musica\poze\membri";
        var expectedfile1 = $@"{expectedParentFolder}\Zuberoa Aznárez.jpg";
        var expectedfile2 = $@"{expectedParentFolder}\Gorka Elso.jpg";

        var fs = new Files();
        fs.SetFiles(new string[]
            {
                expectedfile1,
                expectedfile2
            });

        Assert.AreEqual(expectedParentFolder, fs.ParentFolder);
        Assert.AreEqual(2, fs.FileList.Count);

        Assert.AreEqual(expectedFile1, fs.FileList[0].Path);
        Assert.AreEqual(expectedFile2, fs.FileList[1].Path);
    }    

    [TestMethod]
    [ExpectedException(typeof(ArgumentException))]
    public void SetFiles_FilesNotInTheSameFolder_ExpectedException()
    {
        // 3rd call to SetFiles. Invalid

        // set to invalid structure (files not in same folder)
        // and expect throw
        // and no change

        var validParentFolder = @"c:\C:\muzică\folder1";
        var validFile1 = @"c:\C:\muzică\folder1\file1.txt";

        var invalidFile1 = @"C:\muzică\folder1\file2.txt";
        var invalidFile2 = @"C:\muzică\folder2\file2.txt";

        var fs = new Files();
        fs.SetFiles(new string[]
        {
            validFile1
        });


        fs.SetFiles(new string[]
            {
                invalidFile1,
                invalidFile2
            });

        // test that fs was not modified

        Assert.AreEqual(1, fs.FileList.Count);
        Assert.AreEqual(validParentFolder, fs.ParentFolder);

        Assert.AreEqual(validFile1, fs.FileList[0].Path);
    }
}