One of my previous post was talking on how to get a Free .com or .com.ng domains names. Actually, someone can acquire domain names for free with the steps i explained.
Now domain names also play a role and can affect your ranking to be high or low on google. As i also explained in one of my post that country domains can ranks better than normal tld domain if they both target on that contry with equal site quality and backlink.
To answer the question if free domain names can influence your ranking, yes, sure. It can influence your rank to be higher or lower, for example, some of my blogs with free domain ranks better than others who purchase theirs. Surprising!!. But am not talking about .tk, .ga, cf, domains here, this domain names ranks very low on google, am talking about maybe, some domains given as gift from webhosting company like namecheap or any other company that offers free domain.
But am talking about .com, .ng, .org, .net domain names you acquired freely. It has no difference from a paid .com, .net, .ng domain. If you had acquired a free domain from my steps apart from using .tk domains, then you have nothing to worry about your seo, just improve post quality and backlinks to domain to improve search engine ranking and domain authority because google like authoritative websites and blogs.