Alsace or Luberon

To me, the villages of the Luberon felt like we were living inside a Williams-Sonoma catalog. Alsace felt like we were living inside a gingerbread house. I wish you had time for both regions. I loved them both.

If you love sweeter wines more than drier wines, I would go with Alsace. Otherwise, I would go with Luberon.

Since it's really an apples or oranges choice, you could look at temperatures, your activities, and your tolerance for heat.

I love the Luberon and I, personally, would choose it over Alsace. But my recommendation, given what I read of your interests, is the opposite. Alsace has the better wine and the safer biking (wider roads and dedicated roads). Also, it offers more variety than the Luberon. Luberon villages are beautiful but, even though each one has its own identity, they could feel "samey" after a few days. Whereas Alsace has real towns and cities besides the villages.
As an added bonus: a car is a necessity in the Luberon, less so in Alsace (especially if you're ok biking 5-10 miles to a village!).

Thank you everyone. I was actually more worried that the villages in Alsace would start to look the same after awhile.
Does Alsace feel as authentic? My initial concern looking at photos is that it is almost “too perfect” looking… too Gingerbread housey… and I can’t tell if that is just authentic Alsace or if it’s all tourism.

Riquewihr really has a TON of tourists, but otherwise I would say the wine villages are "authentic". Renovated and manicured (just like the Luberon villages), but not reconstructed or fake.
And in the Luberon, if you're tired of visiting villages, you have little left to do (unless you go visit the rest of Provence, but for example Avignon is a one-hour drive away from Roussillon or Gordes, so it's not quick). In Alsace, you have Colmar, Strasbourg, Germany even...

Ok two more questions…
Is there one region that might be more relaxing or enjoyable after a week in Paris? We are looking for slow pace.

Finally, if you spent a week in the Luberon besides touring villages, is there anything else nearby you would recommend to do that is more active?

Lubéron might be the more relaxing region of the two. The largest town, Apt, has barely 10,000 inhabitants: compare with Colmar, 70,000 or Strasbourg, 500,000.
However, anywhere can be relaxing if you take it slowly.

As for active pursuits in the Luberon: you can cycle if you're ok with the narrow roads and hills (there is a greenway in the plain, but it is not particularly scenic). Also, there is some hiking but it is definitely not the best hiking in Provence. So it would be better to move east towards the Verdon (Moustiers Sainte Marie) for a couple of days, which has excellent hiking as well as water-based activities on the lake Sainte Croix.

I looked at the area around Verdon but the lavender fields and olive trees of the Luberon just appear more to be what I find the most beautiful.

If staying in the Luberon, could you recommend a nice village that is very beautiful, especially to walk around in the evenings, has some restaurants and coffee shops but isn’t over populated with tourists?

The village with the most restaurants is Gordes, by far, but it is also the most touristy. Roussillon also has plenty of places to eat...and plenty of tourists. In both cases, you'll have far fewer tourists in the evenings.
But if you want a place less "discovered", I really enjoyed Saignon, which I discovered in May. The location is stunning, and it has a couple of cafés and restaurants, and it is very close to Apt if you want more. Also, the Claparèdes plateau a little bit to the west has the best lavender fields in the area, in my opinion.
As another alternative, Ménerbes is more touristy than Saignon, but less than Gordes and Roussillon, and it is reportedly quite lively. It is also a bit faster to travel to other parts of Provence from Ménerbes than from Saignon. It happens to be one of the few Luberon villages that I have never visited, though.

This said, some of the most beautiful (and popular) lavender fields in Provence are actually just west of the Verdon, in the area between Moustiers and Valensole, so do not discount that area on those grounds alone!

Wow! I have to thank you, I have been on several travel forums trying to get some answers and you were the first person who really hit it spot on. Saigon it’s exactly what I am looking for, especially in regard to how scenic it looks and also in proximity to a larger village. I really appreciate the recommendation! Are there any taxi cabs out of Apt that would go to Saigon? I only ask in case we wanted to go out and eat and have some wine in the evening without worrying about driving home.

My last question - if Based in Saigon what are some other “must see” villages or sites in the area that you’ve discovered, or even perhaps some beautiful road names to bike down, in this area?

You're welcome!
I have no firsthand experience of taxis in Apt, but the town is large enough to have a few taxis, and it's only 3 miles away. Unsure how to arrange them, sorry.
Worst comes to worst... Apt is a 45-minute walk down the hill, a 1 hour hike back up, on a dedicated path.
Apt would also be the place where you'd have to rent bikes - preferably electric given the terrain. The road between Apt and Saignon is steep, but wide; I would feel safe on it.
I also have to warn you that Saignon has less accommodation than I thought. There is an inn with mixed, but improving, reviews (Auberge du Presbytère), and one or two B&Bs (perhaps more).

Regarding roads:

• the D232 west of Saignon is a true gem, passing through several lavender fields on its way to Bonnieux, and travelling on a plateau with nice views. It is worth going all the way to Bonnieux, which has several inviting terraces with a great view over the plains.

• I mentioned a greenway west of Apt ("voie verte du Calavon"): it is not very scenic but it is easy to bike on, and it provides good access to the roman bridge at Pont Julien, and further on to the village of Goult a short distance up on the hill (take the D105 from Lumières on the way up, not the D145 which is nastily steep even with an e-bike).

Regarding villages: from Saignon, you can easily visit all the "usual suspects" (Roussillon, Gordes, etc.), but you are very close to two lesser-visitied villages: St-Martin de Castillon and Caseneuve across the valley. Those two are worth a visit - they are small, so it will be quick, but they are delightfully peaceful.