SQLSTATE[23000]: Integrity constraint violation: 1062 Duplicate entry  query was: INSERT INTO `catalogrule_product` (`rule_id`,`from_time`,`to_time`,`website_id`,`customer_group_id`,`product_id`,`action_operator`,`action_amount`,`action_stop`,`sort_order`,`sub_simple_action`,`sub_discount_amount`) VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?, ?),

Solution :

Backup the table catalogrule_product.
Truncate it.
Run the reindex process from the command line.
If something goes wrong, just restore you table.