The easiest solution would seem to set up a template for this. But if you
want to do it in VBA, the following variation on your code works:

Sub test()
Dim i As Integer
For i = 1 To ActiveDocument.Sections.Count
   With ActiveDocument.Sections(i)
       .Footers(wdHeaderFooterFirstPage).Range.Delete
       ActiveDocument.Fields.Add _
       Range:=.Footers(wdHeaderFooterFirstPage).Range, _
       Type:=wdFieldEmpty, Text:= _
       "FILENAME  \* Lower ", PreserveFormatting:=True

      .Footers(wdHeaderFooterPrimary).Range.Delete
      ActiveDocument.Fields.Add _
      Range:=.Footers(wdHeaderFooterFirstPage).Range, _
      Type:=wdFieldEmpty, Text:= _
      "FILENAME  \* Lower ", PreserveFormatting:=True

      .Footers(wdHeaderFooterPrimary).PageNumbers.Add _
      PageNumberAlignment:=wdAlignPageNumberCenter, FirstPage:=False

End With
Next i
End Sub

Note that when you add a field, you can use any Fields collection (I used
ActiveDocument.Fields just to make the line a bit shorter), but the Range
parameter of the Add method must carefully reference the Range object to
which you are adding the field. (In particular, you cannot use
Selection.Range.)