Supported hiking tours

You might look at Back Roads and Mac’s Adventures.

Not what you are looking for. Solo or Guided, but not Supported. Thought you might want to file it away. If it ever does interest you I might know someone who might be able to to assist ... not sure, never asked before. https://peaksofthebalkans.info/

And here is a related one day hike to maybe file away. I've been at both ends, but not the middle LOL. For this i do know someone who can facilitate the start and end.

I've done three walking holidays, two 100-mile-long hikes in Ireland -- one 1999, the other in 2010 -- and a 75-mile-long hike in Lake District of England earlier this year. The companies I hired prebooked B&Bs and transported my main bag from hotel to hotel; one chose my trail. The companies I used -- Ireland Walk Bike Hike and Orbis -- apparently do not operate in France and Austria.

Here are some walking holiday tour organizers for France:

• Walkers Britain & Europe: https://www.walkersbritain.co.uk/france
• Macs Adventures: https://www.macsadventure.com/us/
• Ramble Worldwide: https://www.rambleworldwide.co.uk/europe/france
• Utracks: https://www.utracks.com/walking/self-guided-walking/france
• Responsible Travel: https://www.responsibletravel.com/holidays/france/walking

Google "Austria Walking Holiday Operators" for that country.

Here's a trip report from my recent hike in England: https://community.ricksteves.com/travel-forum/trip-reports/a-75-mile-hike-in-the-lake-district

Did you try Sierra Club? They do one:
https://outings.sierraclub.org/trip/Traversing-Spanish-Pyrenees?id=27457A
Since you're in Seattle, you could also ask at the Mountaineers:
https://www.mountaineers.org
They do one in the Balkans as suggested by Mr. E:
https://www.mountaineers.org/activities/activities/global-adventure-trek-the-peaks-of-the-balkans-loop-through-the-accursed-mountains-of-albania-montenegro-and-kosovo-1

Can personally vouch for On Foot Holidays from the UK. Have done several trips and they have all been excellent (routes, logistics, accommodations etc)

https://www.onfootholidays.co.uk/routes/dolomites/

Self-guided walking and hiking tours are abundant and a great idea. One of the absolute classics is walking around Mont Blanc.

One thing I would consider if I were you is that a long walk even through a place like a river valley in country areas is about as satisfying as high mountain single track. I love Alpine areas, and if you want to walk up and down mountains I would suggest the Dolomites. It is also joyfully awesome though to walk through more populated areas with some more infrastructure like the Salzkammergut, Alsace, or the Douro Valley. You going to still get a ton of lovely exercise and views, and encounter more villages and wineries and infrastructure and that sort of stuff. And if you need to, you can usually just get an Uber.

I know the thing is it takes some more planning, but don't be shy about packing quite light and taking a trekking backpack and just walking from place to place on your own. It's much cheaper and you get a lot of freedom to go wherever you feel like or change your mind.

But self-guided is quite reassuring, so not at all a bad way to get started. Have a lovely walk

I took this tour last September, including the offered pre-tour stay in Venice.

Guided-By.com/high-dolomites
Reiner is a delight, the Dolomites are fabulous, and I enjoyed the mix of huts and hotels. There are definitely some rigorous parts, but I was pleased with my accomplishments and was quite happy to have been on this trip.