The word for hamburger in French is simply hamburger.
While it may seem surprising that the term is the same in both languages, it reflects the global influence of fast food. In France, you will find that many common food items retain their English names, especially those associated with American cuisine.
Additionally, you may hear the term hamburgé used colloquially, but using hamburger will be understood in any context. It’s always interesting to see how language evolves and adapts with cultural exchange!