One thing I did not delve into but JohnShelby did is the Catholic concept of anullment. We believe once a contract is entered into (a vow) then it is unbreakable. Even if you get a civil divorce (which is allowable), you are not free of your vow to God. You therefore are not free to remarry (except your original spouse or if your original spouse dies and you are then a widow/er). There are some very rare exceptions allowing a religious divorce (meaning it is found that the vow was valid and you are allowed to still divorce and remarry.)
However, there are certain conditions that could be present that would make the contract invalid from the beginning. It was never valid in the first place. All marriages are presumed to be valid unless a finding to the contrary is found by a church court (tribunal). This includes common law marriages in places that have them (meaning no cermony or one where just a couple friends witness or whatever other such circumstances that equal just two people saying they are married).
As JohnShelby pointed out, the intentions of one or both parties at the time of the vows and even what it is they vow to can mean a valid marriage did not occur in the first place. It is presumed it was valid. But a tribunal can say it was not. Fear, duress, an intention of excluding God from the marriage, immaturity to the point of being unable to comprehend what one was doing, etc. all can make a tribunal say no marriage existed.
Simply having it outside a church is not in and of itself cause. My bishop gave us permission to have our wedding in a secular location because of very high family tension. They would not approve of the wedding if it was in a Catholic Church, we refused to have it in theirs. They later decided they wouldn’t support the wedding wherever it was so we decided to have a full nuptial Mass at church anyway.
Also, it is allowable to have a non-Catholic clergy member officiate the wedding if there is sufficient reason (which is a pretty low threshold usually). Then the rules on what you can do must abide by the other clergy member’s. So if he lets you have it outdoors, it is still valid.
In northern Canada, a nun is allowed to officiate at weddings because there is no other representative of the church around to do so.
There are a lot of exceptions to the rules. The marriage would be presumed to be a valid one. However, if it was taken in front of a tribunal, the intent of the parties (since neither are Catholic and therefore are not expected to marry in the Catholic church) would be scrutinized the most. I wouldn’t be surprised if it was determined that a valid marriage did not occur. It would depend, as JohnShelby pointed out, on the intent of the bride and groom and their particular circumstances.