Compare two CSV file using PowerShell and return matching values faster

I would read the file you're using for lookups and then create a HashTable for that. HashTables are very efficient for doing lookups.

Try something like this, assuming you don't have any duplicates in in FileContentMagic:

# Use any character here which is guaranteed not to be present in the Matricule, Nom,
# or Prenom fields
$Delimiter = '|'

# Read the FileContent Magic into a HashTable for fast lookups
# The key is Matricule|Nom|Prenom
# The value is IGG joined with a forward slash
$FileContentMagic = @{}
Import-Csv -Path $FileContentMagicFileName | ForEach-Object {
    # Here we build our lookup key. The Trim() is just in case there's any leading or trailing
    # whitespace You can leave it out if you know you don't need it
    $Key = $_.Matricule.Trim(), $_.Nom.Trim(), $_.Prenom.Trim() -join $Delimiter

    # Since we only need the IGG value joined with a /, we'll just keep that
    $Value = $_.IGG -join '/'
    $FileContentMagic.Add($Key, $Value)
}

$FileContentIMM = Import-Csv -Path $FileContentIMMFileName

$FileCheckTrue = foreach ($item in $FileContentIMM) {
    $Key = $_.Matricule.Trim(), $_.Nom.Trim(), $_.Prenom.Trim() -join $Delimiter

    [PSCustomObject]@{
        'MATRICULE' = $item.'Matricule'
        'IGG'       = if ($FileContentMagic.ContainsKey($Key)) { $FileContentMagic[$Key] } else { 'noSet' }
        'NAME'      = $item.'Nom'
        'FIRSTNAME' = $item.'Prenom'
        'SERVICE'   = $item.'Service'
        'Immeuble'  = $item.'Immeuble' 
        'Niveau'    = $item.'Niveau'
        'Loc.'      = $item.'Loc.'
        'PDT'       = $item.'PDT'
        'Occ.'      = $item.'Occ.'
        'Site'      = $item.'Site'
    }
}

Also, any time you're using += to concatenate an array, you're introducing a significant performance penalty. It's worth it to avoid using it because each assignment creates a new array, copies the entire array over with the new item, and then discards the old array. It's very inefficient.

If $FileContentMagic contains duplicate keys, then you should change how the HashTable is loaded to:

$FileContentMagic = @{}
Import-Csv -Path $FileContentMagicFileName | ForEach-Object {
    $Key = $_.Matricule.Trim(), $_.Nom.Trim(), $_.Prenom.Trim() -join $Delimiter
    if (!$FileContentMagic.ContainsKey($Key)) {
        $Value = $_.IGG -join '/'
        $FileContentMagic.Add($Key, $Value)
    }
    else {
        $FileContentMagic[$Key] += '/' + ($_.IGG -join '/')
    }
}

I would simplify this, but the changes shouldn't affect the time to process much. The only optimization I've done is changed $filechecktrue to a List which is more memory-efficient.

Not sure if this is actually the slow part of your script. That would require $fileContentMagic to be a VERY large array.

$filechecktrue = New-Object System.Collections.ArrayList

foreach ($item in $fileContentIMM) 
{
    try
    {
        $Matricule = $item.'Matricule'
        $name = $item.'Nom'
        $firstname = $item.'Prenom'

        # find first matching row in $fileContentMagic using wildcard
        $objMatch = $fileContentMagic | Where-Object { $_.'Matricule' -eq $Matricule -and $_.'NOM' -eq $name -and $_.'PRENOM' -eq $firstname}

        #Create results object with common properties
        $o += [pscustomobject]@{
            'MATRICULE' = $item.'Matricule'
            'IGG' = 'noSet'
            'NAME'  = $item.'Nom'
            'FIRSTNAME' = $item.'Prenom'
            'SERVICE' = $item.'Service'
            'Immeuble'= $item.'Immeuble' 
            'Niveau' = $item.'Niveau'
            'Loc.' = $item.'Loc.'
            'PDT' = $item.'PDT'
            'Occ.' = $item.'Occ.'
            'Site' = $item.'Site'
        }

        ##### check if any match found 
        if ($objMatch)
        {
            #if not null, set IGG value. No need for foreach as $item is already a "foreach-value".
            $o.IGG = ($objMatch.'IGG' -join '/')
        }

        #Add result to arraylist
        $filechecktrue.Add($o)
    }
    catch
    {
        "ERROR: Problem reading line - skipping :" | Out-File $LogFile -Append -Force
        $item.nom + $item.prenom + $item.service| Out-File $LogFile -Append -Force
    }
}

Your first foreach returns a single $item-object on every iteration, so it's nonsense to again use a foreach on $item inside the code block (twice).

Try this (redundancy removed):

foreach ($item in $fileContentIMM) {
    try {
        # find first matching row in $fileContentMagic using wildcard
        $objMatch = $fileContentMagic | where { $_.'Matricule' eq $item.'Matricule'
                                           -and $_.'NOM' -eq $item.'Nom'
                                           -and $_.'PRENOM' -eq $item.'Prenom'}


        ##### check if any match found 
        if ($objMatch -eq $null) {
            $IGG = 'noSet'
        } else {
            $IGG = ($objMatch.'IGG' -join '/')
        }
        $filechecktrue += [pscustomobject]@{
            'MATRICULE' = $item.'Matricule'
            'IGG' = $IGG
            'NAME'  = $item.'Nom'
            'FIRSTNAME' = $item.'Prenom'
            'SERVICE' = $item.'Service'
            'Immeuble'= $item.'Immeuble' 
            'Niveau' = $item.'Niveau'
            'Loc.' = $item.'Loc.'
            'PDT' = $item.'PDT'
            'Occ.' = $item.'Occ.'
            'Site' = $item.'Site'

    } catch {
        "ERROR: Problem reading line - skipping :" | Out-File $LogFile -Append -Force
        $item.nom + $item.prenom + $item.service| Out-File $LogFile -Append -Force
    }
}