We are planning to cycle both, later this month. We found some self-guided cycling resources and - for better or worse (time may tell) we chose one vendor over another. Self guided, meaning THEY book the hotels and transfer your bags from one to another. You cycle from one to another. We are choosing e-bikes, rather than road bikes.
One initial source I found was "freewheeling france" which appears to be an independent reviewer of various options; the reviewer is based in the UK. https://www.freewheelingfrance.com Like Mystique, I think that this is a great first resource to begin your search.
My query to this forum, last summer (https://community.ricksteves.com/travel-forum/france/bike-touring-in-france-operator-suggestions), resulted in a positive review for discoverfrance, https://www.discoverfrance.com/european-tours-destinations?gclid=EAIaIQobChMIkr6N_Jrh_gIV8xJ9Ch1nvADyEAAYAiAAEgIKNvD_BwE#france
However, we have chosen le velo voyageur instead, in part because it is a small, women owned business with a nice appearing business culture. https://www.levelovoyageur.com/en/ We found le velo voyaguer on freewheeling france. So far, dealing with them over the phone and via email, making adjustments to their offerings to suit our needs (an extra day here at Montignac in the Dordogne, a six-day seven-night "piece" of their 14 day Loire trip, there) has been great, Their "app" (which we were able to download now that we are within 30 days of departure) looks quite good.
Self-guided touring is less than 1/2 the price of other operators' "guided" tour options.
I have also found that it is useful to look up reviews on Trip Advisor once I have narrowed the field of options in order to get a 'feel' for the reviews available there.
FWIW, Our Dordogne loop is Bergerac-LeBugue-Montignac (2 nights)-Sarlat (2 nights)-Belves-Bergerac. Loire is linear: Blois-Amboise (2 nights)-Tours-Azay le Rideau-Chinon-Saumur.
(PS - J'ai vu Bruno, peut-etre un ou deux fois)