We have been using Expedia, etc. to search for flights, but are there airlines that are not visible on those platforms, as is the case with Southwest in the US?
For planning, I like Matrix ITA website. It is the old travel agent flight planning software and as it doesn't sell flights, it does sometimes have airlines not listed on 3rd party selling sites. I have seen some of the budget European airlines on it. Google did buy it out some time agon, and prompts to use Google flights, but I still prefer Matrix as I think it offers more options for less straightforward routes and countries.
I like to use https://www.skyscanner.com/ for flights within Europe. I book directly through the airline after reading the fine print carefully to pay for the type of ticket I want, ie, cancellable, checked bag, seat selection.
plus one Skyscanner, comprehensive, intuitive interface, fast and you can search entire countries not just individual airports.
You don't mention where you are going, but don't forget to consider trains as well.
Thanks for these answers so far. Trains are our first choice, but sometimes air makes more sense.
Fundamental tool for trains is www.seat61.com I also have used Trainline, especially for the French system.
Skyscanner has been good for budget airlines that may not appear in North American search sites. As a backup for Google/Matrix I sometimes use www.cheapoair.com but only for information.
I use google flights. All airlines show up there.
Google flights works for me to.....
Trains are our first choice
Great!