Thx Gmayor for your answer.

I added few lines to my code, so when the log file is open the file fullname, the user name , and the date are automatically filled, the user just need to add a description of the modification.
base on that the simplest way i think would be the
start Excel open the log, write the data, save the log and close it
excel file is simply a 4 columns sheet with file fullname(of the monitored file), the user name , the date , and modification description

Private Sub Workbook_BeforeSave(ByVal SaveAsUI As Boolean, Cancel As Boolean)

Dim Confirm As VbMsgBoxResult

Application.EnableEvents = False

Cancel = True

Confirm = MsgBox("Do you need to updtate de log book?", vbYesNo)

If Confirm = vbYes Then

    Set monitoredDoc = ThisWorkbook
    
    Set historyWb = Workbooks.Open("C:\Users\Vincent\Desktop\Excel-Malin\test1.xlsx")
    Set historyWks = historyWb.Worksheets(1)

    Dim chemin As String

    chemin = monitoredDoc.FullName

        With historyWks
            nextRow = .Cells(.Rows.Count, "A").End(xlUp).Offset(1, 0).Row
        End With
        With historyWks
            With .Cells(nextRow, "C")
                        .Value = Now
                        .NumberFormat = "mm/dd/yyyy hh:mm:ss"
            End With
            .Cells(nextRow, "B").Value = Application.UserName
            .Cells(nextRow, "A").Value = chemin

        End With


    Else

    ThisWorkbook.Save

End If

Application.EnableEvents = True

End Sub