My family and I are planning to travel from Dover (UK) to France, then to the Netherlands by car. Because 3 of us (out of 6 persons) don’t hold British citizenship, we applied for a Schengen visa. Luckily we have our Schengen visas now, but the problem is that we want to go a day before the Schengen visa starts. Do you think this will cause a problem?
You will not be able to enter the Schengen area before midnight (at the beginning) of the date of validity, because your visa will not be valid.
If you want to begin your trip the day before, you should be able to change your plans to take an overnight ferry direct to the Netherlands.
You should also be able to take a ferry from another port to France before midnight that arrives in France after midnight. Because of the time difference, for example, a 90-minute journey starting at 21:35 arrives the next morning at 00:05.
However, this probably won't work from Dover because of the juxtaposed immigration controls. In Dover, you will encounter French immigration before you leave, so you will probably not be allowed to proceed until after midnight.
None of the above applies if the family members holding the visas qualify for freedom of movement under directive 2004/38/EC based on their relationship with one of the British citizen travelers. In that case, they should be allowed in regardless of not having a visa (under the directive, a visa should be issued on the spot by the border officer, but in practice it seems that this does not happen, and it is even more unlikely when the traveler has a visa that will become valid the next day).