Doable ... theoretically, yes. But it's about three and a half hours on the train one-way.
For me this would be a NO.

taking the train to Bruges from Paris
 

Yes, all the trains from Paris to Bruges and back require a change in Brussels.
Thalys from Paris-Nord (7:25) to Bruxelles-Midi (8:47), then a local train to Bruges (Brugge), dep. 8:56 - arr. 9:54 (or any later train).
Book on www.thalys.com

Be sure to book your Thalys ticket all the way to Brugge; there's no need to get a separate Brussels-Brugge ticket, it's all on the same Thalys ticket.
While you have a seat reservation for a fixed Thalys train on the Paris-Brussels part, once in Brussels Midi you can take any local train to Brugge. There is no seat reservation on the local train.
You can find out in advance which platform your train to Brugge departs from. If in doubt, just ask someone. It's all signposted so you shouldn't have any problem.

IMHO, the best time in Bruges is after the daytrippers leave. It really is a fairy tale town when the lights come on and you are walking the streets alone. It is a totally different place than during the day.

That's helpful information for the trains; thank you.

I'm sure that's true, but I only have an opportunity for a day trip.

I would've loved to see Bruges at night but we only had the opportunity to see it as a day trip. The Thalys train ride was comfortable and never once did we say afterwards, "Wow that was too rushed". We are both in our 50's and thought the day trip in and out of Paris was great. We climbed 366 steps up the bell tower, had a beer flight at Beerwall, shopped, enjoyed a late afternoon mussels meal and did a canal boat cruise. Get there before noon, leave late evening. You won't regret it.

But it has been explained how you CAN be there after the day trippers abandon the place. The coach tours are on the way out of town by 4PM (most even earlier). So if you take a morning train and then stay through dinner and take an evening train back to Paris you will see two completely different cities - one version between 10 AM and 4 PM . . . and a different one in the early evening.

Sorry but I skipped much above. DH and I took a bus day trip from Paris to Bruges. We didn't have enough time to see the lace-makers at the convent (possibly not there anymore) but felt we had enough time for highlights: boat trip, Michelangelo sculpture, city center and city hall. Lunch on our own. Except for all the excellent information the guides provided, and someone else schlepping for all tickets, what janisj wrote makes sense.

I agree with some of the others that if you are going to make the effort to go there, stay until the town lights up. You don't need to stay long.

I'll give you an off-the-wall comparison: Toledo Spain is a common daytrip from Madrid and it's a nightmare of tourist madness during the day; when darkness falls and daytrippers have fled, it's sheer magic.

And I so hope you find a copy of "In Bruges" to watch.
Enjoy,
AZ