if you and/or her have family coverage both are treated as having family coverage. then you have to look at the deductible under your health plan and her health plan. the lower of the two must be used to determine if both of you are covered by a HDHP. if not then neither can contribute to an HSA because of the family coverage rule. so your HDHP can not have family coverage and neither can hers if you want to contribute to your HSA under self-only coverage.
you did not say why your spouse would be HSA ineligible. if your spouse was not eligible for a HSA because she had a FSA a/c, then if that FSA CAN be used to pay your doctor or hospital bills then you have non-HDHP coverage which disqualifies you from contributing to an HSA. if her plan is non-HDHP and covers you that also disqualifies you from contributing to an HSA
