I received a letter from my parish (county) zoning office tell me that I have a travel trailer to close to the property line.

You need to ask the zoning office to give you a copy of the zoning ordinance they are enforcing. There may be an ordinance that is different from the property restrictions. If they can't show you the ordinance then you can simply keep it there, but my guess is that there is some ordinance. You also need to see if it is being violated by someone else in the neighborhood. If so, and they have been in violation for some time, then a court would consider that portion of the ordinance as having lapsed for failure to be enforced. Read the zoning ordinance carefully to see what it applies to, when it was enacted, and what area of the parish it applies to. Some only apply outside towns and cities. If you are inside the city limits, the city would have to agree with the ordinance, or would have agreed to be bounded by the zoning commission. Most large cities have their own zoning and planning departments.