Unless I've misunderstood, I fancy the update SQL should look like this:
[vba]
sSQL = "UPDATE tbl_Test " & _
" SET FieldName3 = 'None' " & _
"WHERE FieldName1 = '" & Me.TextBox1.Text & "' AND FieldName2 = '" & Me.TextBox2.Text & "'"
oRS.ActiveConnection.Execute sSQL
[/vba]

In other words, at the moment you're only updating the table where the actual value of FieldName1 is literally "Me.TextBox1.Text", rather than the value of Me.TextBox1. You missed some of the concatenation, easy mistake to make!!