When are you going? Many tickets are not available until 4-6 weeks before a date. The official website to order tickets for most of the caves is monuments-nationaux.fr. It is the site for the Centre des Monuments Nationaux. At the upper right corner you will see the letters "fr" with an arrow pointing down. Click on that and you will see "en" and "es". Then click on "en" for English. A page will appear "Find a Monument". Below that are options. Choose "Department" and in the drop-down box click on "Dordogne". Scroll down and click on "Prehistoric Sites of the Vezere Valley". You may have to reclick on a language option again (upper right corner). Font-de-Gaume will appear. Click on that. Other places are there also.
Lascaux IV (the newest reproduction and a fantastic job!) official website is lascaux.fr/en/. This is for English. I have been to Lascaux II, over 20 years ago, and it was very nice, but this is really impressive, with lots of additional info on prehistoric caves, etc. It is much easier to get tickets for this and they have quite a few tours in English. (You must go in with a guide.)
Font-de-Gaume is the real deal, so tours are limited and are in smaller groups (about a dozen persons, max). There was only one in English per day when we went in 2023, but sometimes there are two. Because they are harder to come by I started checking daily almost two months before the date we wanted, and jumped on buying the tickets as soon as they came up. (We were seven in our group, so I was diligent in getting those tickets.) This was for early June, before school holidays, and midweek. Weekends were harder. (I believe they were closed on Saturdays. Go figure!) Remember that if they aren't available yet, sometimes it looks like they are sold out for those days.
FYI, the National Museum of Prehistory in Les Eyzies might interest you. It was closed when we went to Font-de-Gaume, which is very near Les Eyzies.