What can I do against a competitor copying my software?

Copyright infringement is actually one of the easier cases to prove because as registered owner, you have providence (proof of how you created it) and comparison whether identical binaries or substantially similar with superficial changes can be trivial to demonstrate (though compilations or mixed use becomes increasingly complicated). What becomes more harder is separating the expression from idea where they've reimplemented the functionality via clean room techniques (which is legitimate). So whilst it is easy to claim, there are certain defenses (eg fair dealings in Australia like backups) or compatibility/interoperability. There's also a recent Australia law (reminder to self to check progress) that allows SMEs to escape some of the more burdensome contractual adhesion clauses by dominant vendors.

As for evidence, basic property theory, proof of legal ownership, evidence of infringe (eg buying competitor product and showing direct relationship to copyrighted material), perhaps expert opinion on the degree of infringement, evidence that you've asserted your claims against the right legal entity (infringement could be done "unknowingly" by subcontractor) ... as always consult a lawyer if you want to go down the legal route rather than settlement.

In Europe and particularly in France, the evidence of infringement of IP rights such as software, when viewed in a context strictly "tort" naturally leading to judicial action, is facilitated by the implementation of a procedure (French invention!) highly effective which is called "infringement seizure" and ordered by a court president: it is possible to send a bailiff accompanied by a police officer, a computer scientist, a locksmith, an accountant … on the place of the suspected infringement, who will be able to do all investigations on site to identify the origin of the infringement and to assess its extent. The officiating bailiff will be able to take statements and financial papers from officials found there, really grab items including software, copy accounting documents (invoices, purchase orders, delivery notes ...), the computer hard disks, make shots ... subject to not violating the confidentiality of trade secret. It will then be necessary to introduce a proceedings before the competent court which will validate the infringement seizure and make recognize and sanction the alleged facts by the judges. Commercial and so moral damages acan be significant following the violations. The infringement seizure is systematically used regarding patents and software as it can prove materially the infringement. In case of breach of contract context, arbitration may emerge as the "natural" way of resolution and other evidence may be used as testimony, certificates, affidavits and legal opinions with which the Anglo-Saxons are more familiar.