Short answer
Yes. Eating while sitting on the floor, with food on a spread cloth, was the Prophet's ﷺ usual practice and is sunnah. It is not obligatory: eating at a table is permissible (mubah). What matters more is the manner: humility, bismillah, the right hand and not overeating.
Eating on the floor on a dastarkhan (eating cloth) is sunnah and closer to humility. Eating at a table and chairs is mubah, not makruh.
The four schools agree on this.
Explanation
Anas, who served the Prophet ﷺ for ten years, said he never knew him to eat from a raised table (khiwan). When his student Qatada was asked what they ate on, he said: on the sufra, a cloth or leather mat spread on the ground. The Prophet also said that he did not eat reclining.
The point is humility. Sitting on the floor, close together and sharing from one dish, is how a servant of Allah eats, not how a proud person dines. The scholars describe sitting on one or both knees, or with one knee raised, as the posture closest to the Sunnah.
The Prophet ﷺ did not forbid tables. He simply did not use them, and later scholars ate at them. So a family eating at a dining table is not doing anything wrong, and the four schools agree it is allowed. If you want to follow the sunnah, spread a cloth on the floor for some meals, especially with family or guests.
Older people and anyone with knee or back problems should eat however is comfortable; the Sunnah never asks for hardship. The more important manners, such as bismillah, the right hand and eating from what is in front of you, are in sunnahs of eating and eating with your hands.
The evidence
Sahih al-Bukhari 5386
Sahih... ولا أكل على خوان ...
"Nor did he eat from a raised table."
Anas describes the Prophet's habit of eating on a cloth on the ground.
Sahih al-Bukhari 5398
Sahih... لا آكل متكئا ...
"I do not eat reclining."
The humble posture of eating.
Where the ruling is recorded
- al-Fatawa al-Hindiyya, Kitab al-Karahiyya, chapter on eating and drinking. The manners of sitting to eat, and that eating from a table is permitted.
Checked by our team. For a more accurate answer to your own situation, consult a scholar. Quran translation by Sahih International. Hadith Arabic from the standard editions of the six books and the Muwatta, with gradings as recorded there; the English is our own rendering. Spotted a mistake? Tell us.