First of all, thank @NarendraPandey and @nehamishra for the help provided

I have given the solution to my problem, which will then put the solution in case someone can serve you.

I have created a method to obtain the available calendars that are local and those of gmail, the code is the following one:

- (NSMutableArray*) getCalendars {

    NSMutableArray *res =[[NSMutableArray alloc] init];

    EKEventStore *eventStore = [[EKEventStore alloc] init];
    EKEntityType type = EKEntityTypeEvent;
    NSArray *calendars = [eventStore calendarsForEntityType: type];

    for ( EKCalendar *cal in calendars )
    {
        if (cal.type == EKCalendarTypeCalDAV || cal.type == EKCalendarTypeLocal  ){
            NSLog(@"cal nombre:- %@ ", cal.title);
            [res addObject: cal];

        }
    }

    return res;
}

Then to show the list of calendars so that the user can select one and enter the events there, I found that Ihave to use an Action Sheet, although I have seen that it was deprecated according to some forum comments Of ***, so I used UIAlertController, being as follows:

NSMutableArray* cals =  [self getCalendars];

if([cals count] > 0){//Comprobamos que existan calendarios

   UIAlertController *alert = [UIAlertController   alertControllerWithTitle:AMLocalizedString(@"calendar_dialog_info", @"")
          message:nil
          preferredStyle:UIAlertControllerStyleActionSheet];

   for ( EKCalendar *cal in cals )
   {
         UIAlertAction *calAction = [UIAlertAction actionWithTitle: cal.title
         style:UIAlertActionStyleDefault handler:^(UIAlertAction * action) {

         NSLog(@"You pressed button %@ ", cal.title);

         [self descargarCalendario:  cal];
          }];

          [alert addAction:calAction];
   }

   UIAlertAction* cancel = [UIAlertAction
                                         actionWithTitle:AMLocalizedString(@"cancelar", @"")
               style:UIAlertActionStyleCancel
               handler:^(UIAlertAction * action)
               {
                    [alert dismissViewControllerAnimated:YES completion:nil];

               }];

         [alert addAction:cancel];

         [self presentViewController:alert animated:YES completion:nil];
}else{
    NSLog(@"No hay calendarios");
}

Where the [self downloadCalendario: cal]; function is responsible for downloading some events from a web service and adding them to the chosen calendar.

Resulting in the following view to choose the calendar:

And the code to add the event to the selected calendar is:

-(void)addEventOnCalendar: (EKCalendar *) cal{

    EKEventStore *store = [EKEventStore new];
    [store requestAccessToEntityType:EKEntityTypeEvent completion:^(BOOL granted, NSError *error) {
        if (!granted) {
            return;
        }
        EKEvent *event = [EKEvent eventWithEventStore:store];
        event.title = @"Test";

        NSDate *cDate = [NSDate date];
        event.startDate = [cDate dateByAddingTimeInterval:((5*60*60) + (30 * 60) + 15)];
        event.endDate = [cDate dateByAddingTimeInterval:((5*60*60) + (30 * 60) + 15)];

        //event.calendar = [store defaultCalendarForNewEvents];
        event.calendar = [store calendarWithIdentifier: cal.calendarIdentifier];

        NSError *err = nil;
        [store saveEvent:event span:EKSpanThisEvent commit:YES error:&err];

    }];
    UIAlertView *alert=[[UIAlertView alloc]initWithTitle:@"Message" message:@"Event Successfully added " delegate:self cancelButtonTitle:@"ok" otherButtonTitles:nil, nil];
    [alert show];

}

I hope it helps somebody.