Assuming you have Enterprise Edition, and there may be other ways that involve programming skills but barring that the only way I have found I am able to do this is by looking at it as synching up the fields whenever  the Contact record is saved by using a cross object workflow/field update.  I have not done this with Contacts, but have done it with a custom object and have seen it done with Cases.  The workflow triggers every time a record is saved in the custom object and the field update copies an Account field to the field in the custom object record. 

The equivalent in your case would be when the Contact record is saved the workflow would trigger updating Contact/Industry with Account/Industry.

The rule would be on the Contact object and the evaluation criteria would be Every time a record is created or edited  The Rule criteria would be something like LEN( Account__r.Industry ) >= 0       This will make the rule always meet the criteria and always trigger on a Save of a Contact record. 

The field update Workflow would be setup to have the field to update be Industry and The field update formula would be something like Account__r.Industry 

It will not automatically update your 800 records until such time as you again save them though, but it will keep them in synch when they are edited/Saved. 

Hope this helps.  To update them all at once you may need to look at doing a mass update with Data Loader but you would need to create a .csv file with a column with Contact ID and one with Industry.