The historians of Reddit discussed why French fries became such a common pairing with burgers:

• White Castle was the first fast food chain to serve french fries next to burgers in 1921.
• They may have gotten idea from WW1 soldiers returning from Europe who had gotten a taste for fried potatoes in Belgium.
• Fries had the advantage of being cheap to make, were not frequently made at home (since few deep fried), and had a taste that was neutral and complimented meat.
• Moreover they were both fast and cheap to make, and didn’t require cutlery to eat.
• By the time the MacDonalds brothers opened their first restaurant, getting a side of fries with a burger was expected by patrons.

Read more about the history of fast food and French fries over here.

Source: Reddit