Coming from the EU
Personal-use food is generally fine.You can carry meat and dairy for your own consumption. EU-grown fruit, vegetables and plants can also be carried if free from pests or disease.
A suitcase full of food is simple inside the EU, but very different when you arrive from the USA, Great Britain or another non-EU country.
SHORT ANSWER
The key question is where the food comes from, not whether you arrive by plane or car.
You can carry meat and dairy for your own consumption. EU-grown fruit, vegetables and plants can also be carried if free from pests or disease.
This applies to arrivals from countries such as the USA and Great Britain, subject to specific country/product exceptions.
FROM THE USA / GREAT BRITAIN / OTHER NON-EU COUNTRIES
No ordinary personal imports of meat or meat products.
Milk, cheese and other dairy products are generally prohibited.
Up to 20 kg, or one fish if that fish weighs more.
Generally up to 2 kg for products covered by this category.
Special exemptions can allow up to 2 kg if packaging and storage conditions are met.
Many plant products from non-EU countries require a phytosanitary certificate. Bananas, coconuts, dates, durians and pineapples are notable exceptions.
For these food rules, the transport method usually does not change the basic answer. A ham sandwich from the USA does not become legal because it is in checked luggage rather than a car.
FAQ
Generally no. Dairy products from most non-EU countries cannot be brought into the EU in ordinary personal luggage.
Generally no. Great Britain is outside the EU for these rules, and meat products are generally prohibited in personal luggage entering the EU.
Generally yes for personal consumption, including meat and dairy, because both countries are in the EU.