Inexpensive, best way from Stockholm to Paris

Ryan Air does cheap flights, however the airports are a ways out of the city, I don't know how far the airport is from Stockholm most likely an hour, but Beauvais is about an hour bus ride from Paris, the cost of the bus is 13 euros.

At the airports there is information on how to get to the cities, and at Beauvais I knwo for sure you can purcahse the bus ticket right at the airport

Tickets are pretty cheap, check ryanair.com for more details

Both SAS and Norwegian Air Shuttle fly direct to/from Stockholm and Paris. Looking at an arbitrary date in May (5/13-5/20 flying on Tuesdays) you can fly as cheap as 59 euro R/T on Norwegian. SAS was about 132 euro for that selected date, but I didn't look at too many combinations. Norwegian flies into Orly while SAS out of CDG. Ryan Air flies there too, but the airport in Stockholm (Skavsta) is about 100km out of town and I think Beauvais is quite a bit out of Paris. Of course the dates above, you could fly for 198 SEK (which is about 21 euro). You'd have to determine if the cost difference is worth the extra travel time and expense to/from the airport to get that fare.

My wife and I booked Norwegian for our flight this summer from Paris to Stockholm.

Definitely fly. Try to get a flight to Stockholm Arlanda (ARN). The discount airlines fly to Skavsta which they call "Stockholm" despite the fact that is way out.