Check my other comment. I grind using an old timey grinder. Not sure what condition the grinding parts are in as I don't know how they should look new. So your pre-ground should be fine. Probably with a but shorter steep (2-4 minutes?). You biggest issue may be oxidation of your coffee.
You do know you can fake a french press by just putting water and beans in a container, let it steep and once done pour through a fine sieve.