Refinancing a Home Mortgage

Hello All and hope everyone is doing well surviving France :-)

Would anyone be willing to share some advice or experience about refinancing? We took out a mortgage on a flat and then moved to another region for work opportunities. We kept the flat and currently have tenants. Because our new region is quite expensive and our family is growing, I've asked my French husband about possibly refinancing our 20 year mortgage and extending the years to cut down on our monthly out-of-pocket on the home - our tenants do not pay the full monthly mortgage or we'd never be able to rent the place out! He asked our bank and we were informed that we would incur a lot of fees to refinance. In my leftover American capitalistic and optimistic attitude, I said "Then we should find another bank that will buy our loan and waive the fees!"

So my husband scoffed at my plan and told me that no other bank would do that haha. I was able to do this with my house in the US quite easily, and granted we are in a very different place but I still think that other banks would see the financial advantage of competing - and perhaps our bank would waive or cut down on the fees if they felt some competition. Am I missing something here? I've been a bit surprised at the French loyalty for their banks even if they know they're not getting the best terms and rates. Thanks in advance everyone for your insight!