With Sheets("Sheet1").Rows(Fn + 1)
                .Columns(1) = Filename
                .Columns(2) = Sum_L
                 Sum_L = 0 '<<<<<<<<<<<<<<<Add this Line
            End With
Here is how I found it. Left no possibilities to chance! First I performs all calculations by Sheet Formulas, then ran the code until I got a wrong value. Of course it was at the very end. A stupid omission. 

Option Explicit

Sub SamT_4()
    Dim Filename As String
    Dim NameLength As Long
     
    Dim FileNames As Variant
    Dim FileLines As Variant
    Const F As Long = 5 'CSV field number counting from zero
     
    Dim F_Array() As Double
    Dim K_Array() As Double
    Dim L_Array() As Double
    Dim Sum_L As Double
    Dim FName As String
    Dim X
  
     
    Dim Fn As Long 'Fn = Index number for FileNames
    Dim CR As Long 'CR = Column Arrays Index number. Same As Column Row number                                'j
     
    Const FolderPath As String = "C:\TestFolder\" '<<<<<<<<<<    include ending \
     
     '''' Put all the file names in the path in Array
    FileNames = Filter(Split(CreateObject("wscript.shell").exec("cmd /c Dir " & _
    FolderPath & "*.csv /b /s").stdout.readall, vbCrLf), ".")
     
     
     '''' Open one file at a time
    With CreateObject("scripting.filesystemobject")
        For Fn = 0 To UBound(FileNames)
          FName = Mid(FileNames(Fn), 17, Len(FileNames(Fn)) - 20)
          
             ''''Put all lines from one file in Arrays
            FileLines = Split(.opentextfile(FileNames(Fn)).readall, vbLf)
             
             'Compensate for extra vbLf's in FileLines
            Do While FileLines(UBound(FileLines)) = ""
                ReDim Preserve FileLines(UBound(FileLines) - 1)
            Loop
             
            ReDim F_Array(UBound(FileLines))
            ReDim K_Array(UBound(FileLines))
            ReDim L_Array(UBound(FileLines) + 1)
             

            ''''Value F into F_Array
            For CR = 0 To UBound(FileLines)
                F_Array(CR) = Split(FileLines(CR), ",")(F)
                X = Sheets(FName).Cells(CR + 1, 6).Value
                If CDbl(F_Array(CR)) <> X Then
                MsgBox FName & " Cell F" & CR + 1 & " Error."
                 Exit Sub
                End If
            Next CR
             
             ''''Log(F) into Column K
            For CR = 0 To UBound(FileLines)
                K_Array(CR) = Log(F_Array(CR)) / Log(10#) '/Log(10) to match Excel Log Function
                X = Sheets(FName).Cells(CR + 1, 11).Value
                If CDbl(K_Array(CR)) <> X Then
                 MsgBox FName & " Cell K" & CR + 1 & " Error."
                 Exit Sub
                End If
            Next CR
             
             ''''Calculate Formula on Column K, put in Column L
            For CR = 0 To UBound(K_Array) - 1 '-1 to compensate for column formula offsets
                L_Array(CR + 1) = (100 * (K_Array(CR + 1) - K_Array(CR))) ^ 2
               X = Sheets(FName).Cells(CR + 2, 12).Value
                If CDbl(L_Array(CR + 1)) <> X Then
                  MsgBox FName & " Cell K" & CR + 1 & " Error."
                 Exit Sub
                 End If
            Next CR
             
             ''''Sum of Column L
            For CR = 0 To UBound(L_Array)
                Sum_L = Sum_L + L_Array(CR)
                X = Sheets(FName).Cells(CR + 2, 13).Value
                If CDbl(Sum_L) <> X Then
                  MsgBox FName & " Cell M" & CR + 1 & " Error"  .'<<<<<<< Found Error Here
                  Exit Sub
                 End If
            Next CR
             
             '''' Put results in sheet
             
             'Get FileName
            NameLength = Len(FileNames(Fn)) - InStrRev(FileNames(Fn), "\")
            Filename = Right(FileNames(Fn), NameLength)
             
             'Place result
            'With ActiveSheet.Rows(Fn + 1)
            With Sheets("Sheet1").Rows(Fn + 1)
                .Columns(1) = Filename
                .Columns(2) = Sum_L
                 Sum_L = 0 '<<<<<<<<Add this Line
            End With
            
        Next Fn 'Work on next File
    End With
End Sub