I have a process set up on my website through a 3rd party tool whereby if someone downloads an asset, they complete a form and then are automatically loaded into Salesforce as a new Lead. I want to be able to automatically convert any new Leads that are created for Accounts that are already marked with type = Customer in Salesforce. 
 
I have created a Flow that is comparing the Company Name on a Lead to my Account Names with Type = Customer and if true, then calling the Apex class to convert the Lead. However, I would like to amend the Apex Class so that it does not create a new Account, but uses the existing account in the system. So in other words, create a contact only - no account, no opportunity. 

I think I need to use SetAccountId somewhere in the class, but I am not sure where or how to set the Account correctly - can anyone help?

Public class AutoConvertLeads
{
    @InvocableMethod
    public static void LeadAssign(List<Id> LeadIds)
    {
            Database.LeadConvert Leadconvert = new Database.LeadConvert();
            Leadconvert.setLeadId(LeadIds[0]);
            LeadStatus Leads= [SELECT Id, MasterLabel FROM LeadStatus WHERE IsConverted=true LIMIT 1];
            Leadconvert.setConvertedStatus(Leads.MasterLabel);
            Leadconvert.setDoNotCreateOpportunity(TRUE);
            Database.LeadConvertResult Leadconverts = Database.convertLead(Leadconvert);
            System.assert(Leadconverts.isSuccess());
   }
}