database shema

Forgive my silly question, but did you install it on Drupal 6?
What kind/version of database are you using?

#1 Could you try to reinstall it again (I can't reproduce it on my local server)?
Disable FCKeditor module in admin/build/modules, then uninstall it (admin/build/modules/uninstall).

Now login to the Drupal database and run this query:
show tables like '%fckeditor%';
If both tables appear, the error message should be gone.

If there are no tables with such names, let's try to debug it.

• Restart the mysql server (if possible), and turn on query logging for a while (--log) - note that this will slow down your server *.
• Repeat step #1.
• Find SQL queries responsible for creating tables required by FCKeditor (something that contains "fckeditor_settings" and "fckeditor_role"), for example:
  

  CREATE TABLE fckeditor_settings (
  `name` VARCHAR(128) NOT NULL DEFAULT '', 
  `settings` TEXT DEFAULT NULL, 
  PRIMARY KEY (name)
  ) /*!40100 DEFAULT CHARACTER SET UTF8 */
  
  CREATE TABLE fckeditor_role (
  `name` VARCHAR(128) NOT NULL DEFAULT '', 
  `rid` INT NOT NULL DEFAULT 0, 
  PRIMARY KEY (name, rid)
  ) /*!40100 DEFAULT CHARACTER SET UTF8 */ 
  

• Run those queries manually and check what error did you get.

* If you can't enable the general query log, please try at least to check later the database error log file and run the queries I have posted above.

I had this same issue. I upgraded from 5.6 to 6.1. I followed the instructions
in the 6.1/UPGRADE.txt. I replaced the fckeditor 5.x module with the 6.x module
at the end of the edit and re-ran update.php. This did not create the
fckeditor_settings and fckeditor_role tables.

Doing the uninstall, (admin/build/modules/uninstall), fixed for me.

Note, at first I did not use admin/build/modules/uninstall since in 5.6
none of my modules were listed including fckeditor. I then used
admin/build/modules/uninstall, (thanks phicarre), to uninstall fckeditor.
I noted that the modules software sites/all/modules/fckeditor was still
intact. I went back and enabled the module and that created the tables
and got it working.

Closed because of inactivity.