Short answer. Yes, if the union can be undone without injury. Where two things belonging to different owners have been joined and can be taken apart without damage, either owner may demand separation. Where the accessory is far more precious than the principal, separation may be demanded even at some cost in damage.
What the law says
Whenever the things united can be separated without injury, their respective owners may demand their separation.
Civil Code, Article 469 — Separation of United Things. Read the full provision →
Why the law prefers to keep things together
When movable things belonging to different people are joined, the usual rule of accession is that the owner of the principal thing acquires the accessory, subject to indemnity. That is a rule of economic sense: the law would rather compensate in money than destroy value by prising things apart. This article is the exception. It restores each owner's thing where the union is reversible. The controlling word is injury. If the parts come away intact — a component bolted in, a fitting screwed on, a stone in a setting — separation may be demanded and the accession rule does not lock in the result.
The exception for the more precious thing
The second sentence reverses the default in a specific case. Where a thing was united for the use, embellishment or perfection of another and is much more precious than the principal thing, its owner may demand separation "even though the thing to which it has been incorporated may suffer some injury." A valuable gem set into an ordinary ring, or a costly instrument fitted into a cheap housing, is the classic picture. Note the limits carefully: the damage tolerated is some injury to the principal, not its destruction, and the disparity in value must be substantial, not marginal.
Where this actually comes up
The disputes are more ordinary than the language suggests. Equipment or an appliance installed in premises that are later sold or repossessed. A part supplied under a reservation of ownership and fitted into another's machine. A vehicle rebuilt with an engine belonging to someone else. Materials incorporated into a structure by a contractor who was never paid. In each case the first question is factual and often needs a technician rather than a lawyer: can this come out, and what happens to both things if it does? The answer to that question, not the eloquence of the argument, decides the case.
What separation does not settle
Recovering your thing is not the end of the accounting. Good faith and bad faith matter throughout this area of the law, and a party who joined the things knowing they were not his own is treated less generously — indemnity and damages can follow. Separation also does not resolve who bears the cost of dismantling, or the loss of use in the meantime. And the rule governs movables joined to movables; land, buildings and planting are governed by their own provisions. Whether your situation falls under this article turns on the facts, and this is general information rather than advice.