When writing in Dutch you keep the 'D' in de Vries as it would be in the middle of a sentence after Mevrouw, just like in English in the first answer.
Some people, more in Belgium than in NL, use De Vries in all situations, in that case you keep the capital.
Only when it is really the first letter of a sentence you capitalize the 'D' when it is usually a small letter.
My name has two 'middle words' and in most cases they stay small, when at the start of a sentence only the first get capitalized, the actual main word of the name always get a capital.
When writing in a foreign language I keep to the Dutch rules, but people who write in those languages often apply their own rules, so if you look at examples on internet you may find all kind of different rules.