class FileDB
    {
        public string Articule { get; set; }
        public string Naim { get; set; }
        public string Cnt { get; set; }

    }

for (int i = 0; i < artList.Count; i++)
                {
                    for (int j = 0; j <listFileDB.Count; j++)
                    {
                        if (artList[i] == listFileDB[j].Articule)
                        {
                             // Данная операция очень затратна по ресурсам
                        }
                    }
                }

HashSet<string> set1 = new HashSet<string>(artList);
HashSet<string> set2 = new HashSet<string>(listFileDb.Select(a => a.Articule));
var res = set1.Intersect(set2);
foreach (var item in res)
{
// Do whatever you want
}

var selectedItems = listFileDb.Where(item => set1.Contains(item.Articule));

var pairs = from x in artList
            join y in listFileDB on x equals y.Articule
            select new { x, y };