There's a couple of things going on here...
First, your trigger should be bulkified to process any number of objects and not just one. Running on a single item is against Salesforce best practices and can get you in trouble with Salesforce resource limits.
Second, the trigger objects have all of the field values that you are requerying in Lines 4-6 of UpdateContactFromPortalUser.updateContacts....so that query is unnecessary and should be removed.
Third, best practices for unit tests are to insert your own data. You haven't inserted a Contact in your test method, therefore there is no Contact to update. If you were to use an existing user (also against best practices), you would be using a ContactId that won't exist in the test context. I've corrected a few of the issues below in the code example, I hope it helps. The code hasn't been run/tested, but should give you an idea of how you can solve your issue.
 

trigger UpdateContactFromPortalUser on User (after update) {
	// run on every item that meets the condition, not just one
	List<User> usersToProcess = new List<User>();
	for(User u : Trigger.New) {
		if(u.ContactId != null) {
			usersToProcess.add(u);
		}
	}
	
	if(usersToProcess.size() > 0) {
		UpdateContactFromPortalUser.updateContacts(usersToProcess);
	}
}

global class UpdateContactFromPortalUser {
	@future
	public static void updateContacts(List<User> users) {
		// SOQL query is unnecessary here because Trigger objects have all of the data
		// NULL checks already done in trigger code
		List<Contact> contactsToUpdate = new List<Contact>();
		for(User u : users) {
			Contact c = new Contact(
				Id = u.ContactId,
				Email = u.Email,
				FirstName = u.FirstName,
				LastName = u.LastName,
				Title = u.Title
			);
			contactsToUpdate.add(c);
		}
	
		if(contactsToUpdate.size() > 0) {
			update contactsToUpdate;
		}
	}
}

// test class
@isTest
private class UpdateContactFromPortalUserTest {
	static testMethod void testUpdateContacts() {
			// will need to populate Contact with required field values before inserting, FirstName something other than 'Bar'
			Contact testContact = new Contact();
			insert testContact;
			
			// will need to populate User with required field values before inserting, especially ContactId from Contact above
			User u = new User();
			insert u;
	 
	        Test.startTest();
			
	        u.FirstName = 'Bar';
	        update u;
	 
	        Test.stopTest();
	 
	        Contact c = [SELECT FirstName FROM Contact WHERE Id = :testContact.Id];
	        System.assertEquals(u.FirstName, c.FirstName);
	}
}