You can have both an HSA and and FSA, but the FSA is quite limited on what it can be used for if you have and HSA. You can't use it for typical medical expenses, but you can use it for dental and for glasses or contacts. So there is some benefit to having it and deferring some income, you can also rollover $500 at the end of the year.
There's such a thing as a "limited purpose FSA" that only covers things like glasses, dental work, and post-deductible medical expenses so that you don't lose your HSA contribution eligibility. These are commonly offered alongside HDHP insurance.
In the case of a married couple where both spouses work, one has an HDHP, and the other doesn't, the FSA offered to the non-HDHP spouse is unlikely to be one of these limited-purpose FSAs. It is also likely to allow family members to claim expenses against the account, even if they aren't on that insurance plan. This combination is enough to disqualify the HDHP spouse from making HSA contributions. If you want the HDHP spouse to keep being able to make HSA contributions, the non-HDHP spouse needs to decline FSA contributions that year.