If the old fence has been in there for a period of at least ten years, then it may be sufficient to establish title through adverse possession. For instance, see the lexis summary of Weaver v. Helm, 941 S.W.2d 801:
When a dispute arose about the boundary line between the parties' property, the title owner bulldozed the fence and replaced it with one on the line he claimed was the actual property line. The adverse possessors brought suit to determine the actual property line, whether it was the old fence line that had been there for 40 years or the new fence line. The court affirmed the trial court's determination that the adverse possessors were entitled to a portion of the disputed property. The court held that the possessors proved all the elements of adverse possession: possession that was hostile and under a claim of right, actual, open and notorious, exclusive, and continuous for 10 years. The court held that intent to deprive the title owner was shown by the possessor's mistaken belief as to the facts of legal ownership. The court further held that starting with the presumption that the trial court's judgment was correct and the title owner had the burden to show otherwise, the record did not establish that the description of the property in the judgment was not based upon the evidence.
Although, "Of course, a landowner who puts his fence inside his boundary line does not thereby lose title to the strip on the other side. That loss would occur only if his neighbor should take possession of the strip and hold it for the requisite period of years." Harris v. Lynch, 940 S.W.2d 42
So much of it will depend upon the specific facts in your case. If the fence has been relied upon as the boundary line and has been there for more than 10 years, then there seems to be a presumption of that being the line.
I hope that helps. Please let me know if you have additional questions.