Whether your last will and testament, which was written to comply with the laws of the United States and the individual state you live in, will be recognized as valid in a foreign country where you own assets depends on several factors. These factors include the manner in which the will was created and the potentially contradictory inheritance laws of the country in which your assets are located.
Number of Witnesses
The state you live in may require a will to be signed in the presence of two witnesses. But the laws of the foreign country where you own assets might require a will to be signed in front of, say, three witnesses. If you didn't have the correct number of witnesses, then your U.S. will may not be valid in the country where those assets are located.
While a handful of U.S. states recognize nuncupative wills and/or holographic wills, most U.S. states and some foreign countries do not. A nuncupative will is a verbal will that is spoken in front of two or more witnesses, typically while the person wishing to make their inheritance intentions clear is dying. A holographic will is one that is written entirely in the deceased person's own handwriting and signed and dated by that person, with no witnesses.
A will of one of those types that is valid in your U.S. state of residence may not be considered valid in the country where you own assets.
Dispositions to a Spouse and Descendants
Certain parts of your U.S. will may not be valid due to the unique laws of the foreign country where you own assets. For example, many countries have different laws regarding inheritance by a spouse and descendants.
In all U.S. states you are free to leave your property to whomever you want, except that if you are married, most states will require part of the estate to be used for the benefit of your surviving spouse. The only exception is Georgia.
In Louisiana, your direct descendants may be considered "forced heirs" if they are 23 years old or younger or are permanently incapable of taking care of themselves for a mental or physical reason. So long as you haven't disinherited them for a reason the state considers to be legitimate, Louisiana requires these heirs to inherit part of your estate.
Contrast the generally more permissive rules in the U.S. with inheritance laws overseas: Many countries, including France, Germany, Italy, Japan, Russia, and Spain, have forced heirship laws that are more strict than Louisiana's; they require all or a portion of a deceased person's assets to go to a blood relative instead of or in addition to a spouse. This legal requirement can not be avoided by stating a different disposition preference in your will.
Another example of how a U.S. will can create problems in a foreign country is when it establishes testamentary trusts for some or all of the beneficiaries named in the will. This type of trust—which goes into effect only after its creator has died and their estate has been settled—is quite common in the U.S., but it is not in many foreign countries, due mainly to adverse tax consequences for the government. If you wish to leave non-U.S. assets as an inheritance according to the terms of a testamentary trust, the beneficiary or beneficiaries will likely have to pay substantial taxes on them.
Consulting an Attorney
A good U.S. estate planning attorney will recognize that the dispensation of foreign assets you own will need to be addressed outside of your U.S.-based estate plan. Therefore, you will need to meet with an attorney or another legal representative who is familiar with the probate, trust, estate, and tax laws of the country where your assets are located. This new legal professional will determine whether your U.S.-created will can pass muster in the foreign country or if you will need to create a separate will and/or other legal documents in that country to address the final distribution of those foreign assets.