You need to override EmailReceived to know the attachment if any.
Below is the sample code that you can use in your event receiver.
I have added two new columns in my list that will receive the email to know the total attachments and also the file names attached in the email.
TotalAttachments and AttachedFiles.
SPEmailAttachmentCollection attachColl = emailMessage.Attachments;
string AttachedFiles = string.Empty;
int TotalAttachments = 0;
foreach (SPEmailAttachment attach in attachColl)
AttachedFiles += attach.FileName + ";";
Update the list with the columns "TotalAttachments" and "AttachedFiles"
SPItem item = file.Item;
item["TotalAttachments"] = TotalAttachments.ToString();
item["AttachedFiles"] = AttachedFiles.ToString();