Here is the piece of code to get what you are looking for:
Sub ChangeFileFormat()
    Dim strCurrentFileExt   As String
    Dim strNewFileExt       As String
    Dim objFSO              As Object
    Dim objFolder           As Object
    Dim objFile             As Object
    Dim xlFile              As Workbook
    Dim strNewName          As String
    Dim strFolderPath       As String
    strCurrentFileExt = ".xls"
    strNewFileExt = ".xlsx"
    strFolderPath = "C:\Users\Scorpio\Desktop\New folder"
    If Right(strFolderPath, 1) <> "\" Then
        strFolderPath = strFolderPath & "\"
    End If
    Set objFSO = CreateObject("Scripting.FileSystemObject")
    Set objFolder = objFSO.getfolder(strFolderPath)
    For Each objFile In objFolder.Files
        strNewName = objFile.Name
        If Right(strNewName, Len(strCurrentFileExt)) = strCurrentFileExt Then
            Set xlFile = Workbooks.Open(objFile.Path, , True)
            strNewName = Replace(strNewName, strCurrentFileExt, strNewFileExt)
            Application.DisplayAlerts = False
            Select Case strNewFileExt
            Case ".xlsx"
                xlFile.SaveAs strFolderPath & strNewName, XlFileFormat.xlOpenXMLWorkbook
            Case ".xlsm"
                xlFile.SaveAs strFolderPath & strNewName, XlFileFormat.xlOpenXMLWorkbookMacroEnabled
            End Select
            xlFile.Close
            Application.DisplayAlerts = True
        End If
    Next objFile
ClearMemory:
    strCurrentFileExt = vbNullString
    strNewFileExt = vbNullString
    Set objFSO = Nothing
    Set objFolder = Nothing
    Set objFile = Nothing
    Set xlFile = Nothing
    strNewName = vbNullString
    strFolderPath = vbNullString
End Sub
this is the link for XL file format : https://msdn.microsoft.com/en-us/library/office/ff198017.aspx
'-----------------------------------------
A bit Modification:
Check this code, i have only changed its extension name, but please check it with the compatibility... and let me know is it working for you...
Sub ChangeFileFormat_V1()
    Dim strCurrentFileExt   As String
    Dim strNewFileExt       As String
    Dim objFSO              As Object
    Dim objFolder           As Object
    Dim objFile             As File  'Object
    Dim xlFile              As Workbook
    Dim strNewName          As String
    Dim strFolderPath       As String
    strCurrentFileExt = ".xls"
    strNewFileExt = ".xlsx"
    strFolderPath = "C:\Users\Scorpio\Desktop\New folder"
    If Right(strFolderPath, 1) <> "\" Then
        strFolderPath = strFolderPath & "\"
    End If
    Set objFSO = CreateObject("Scripting.FileSystemObject")
    Set objFolder = objFSO.getfolder(strFolderPath)
    For Each objFile In objFolder.Files
        strNewName = objFile.Name
        If Right(strNewName, Len(strCurrentFileExt)) = strCurrentFileExt Then
            strNewName = Replace(strNewName, strCurrentFileExt, strNewFileExt)
            Application.DisplayAlerts = False
            objFile.Name = strNewName
            Application.DisplayAlerts = True
        End If
    Next objFile
ClearMemory:
    strCurrentFileExt = vbNullString
    strNewFileExt = vbNullString
    Set objFSO = Nothing
    Set objFolder = Nothing
    Set objFile = Nothing
    Set xlFile = Nothing
    strNewName = vbNullString
    strFolderPath = vbNullString
End Sub