First thing you need to do is take a good look at the "non-compete" clause. What does it prevent you from doing?
Most of these clauses/contracts merely bar you from toaking employment with an competitor company. In a case like this, you ex-employer will probably still sue you, but the onus rests on him to prove to court that the terms in the contract was a) reasonable b) necessary c) you accepted the terms out of your own free will and know what the effects of them are d) you will proceed to divulge sensitive information to your new employer which will be to his detriment.
You/ your Attorney will have to make the argument that the contract was a) unreasonable due to the excessive restricting effect of you not being able to earn an income in your chosen field b) the protection you former employer seeks is not necessary as you do not possess any privy information of your former employer, namely "trade secrets", client lists. c) at the time of signature of the contract you were not ad idem (in agreement) with the terms.
As a final argument you have to prove put before court that the contract as a whole is contra bona mores (against good public policy) and therefore, in specifically the non-compete clause, is unenforeable.
If however you work in an technical/specialised field, the non-compete becomes very enforceable due to the nature of your employment. A company's development, trade secrets and client lists are all deemed to be an asset worth protection.
15min or part thereof of written consultation : $250.00 please