Powershell script to combine multiple csv files to single one

The following solutions assume that Get-ChildItem *.csv enumerates the files to merge, in the desired order (which works with input files F1.csv, F2.csv, F3.csv in the current dir).

Plain-text solution, using .NET APIs, System.IO.StreamReaderand System.IO.StreamWriter:

This solution performs much better than the OO solution below, but the latter gives you more flexibility. Input files without a Unicode BOM are assumed to be UTF-8-encoded, and the output is saved to a BOM-less UTF8 file named FR.csv in the current dir. (the APIs used do allow you to specify different encodings, if needed).

$outFile = 'FR.csv'
# IMPORTANT: Always use *full* paths with .NET APIs.
# Writer for the output file.
$writer = [System.IO.StreamWriter] (Join-Path $Pwd.ProviderPath $outFile)
# Readers for all input files.
$readers = [System.IO.StreamReader[]] (Get-ChildItem *.csv -Exclude $outFile).FullName

# Read all files in batches of corresponding lines, join the 
# lines of each batch with ",", and save to the output file.
$isHeader = $true
while ($readers.EndOfStream -contains $false) {
  if ($isHeader) {
    $headerLines = $readers.ReadLine()
    $colCounts = $headerLines.ForEach({ ($_ -split ',').Count })
    $writer.WriteLine($headerLines -join ',')
    $isHeader = $false
  } else {
    $i = 0
    $lines = $readers.ForEach({
      if ($line = $_.ReadLine()) { $line }
      else                       { ',' * ($colCounts[$i] - 1) }
      ++$i
    })
    $writer.WriteLine($lines -join ',')
  }
}

$writer.Close()
$readers.Close() 

OO solution, using Import-Csv and ConvertTo-Csv / Export-Csv:

# Read all CSV files into an array of object arrays.
$objectsPerCsv = 
  Get-ChildItem *.csv -Exclude FR.csv | 
    ForEach-Object { 
      , @(Import-Csv $_.FullName)
    }

# Determine the max. row count.
$maxCount = [Linq.Enumerable]::Max($objectsPerCsv.ForEach('Count'))

# Get all column names per CSV.
$colNamesPerCsv = $objectsPerCsv.ForEach({ , $_[0].psobject.Properties.Name })

0..($maxCount-1) | ForEach-Object {
  $combinedProps = [ordered] @{}
  $row = $_; $col = 0
  $objectsPerCsv.ForEach({
    if ($object = $_[$row]) { 
      foreach ($prop in $object.psobject.Properties) {
        $combinedProps.Add($prop.Name, $prop.Value)
      }    
    }
    else { 
      foreach ($colName in $colNamesPerCsv[$col]) {
        $combinedProps.Add($colName, $null)
      }
    }
    ++$col
  })
  [pscustomobject] $combinedProps
} | ConvertTo-Csv 

Replace ConvertTo-Csv with Export-Csv to export the data to a file; use the -NoTypeInformation parameter and -Encoding as needed; e.g.
... | Export-Csv -NoTypeInformation -Encoding utf8 Merged.csv